exercise 22(a) page:279 - byju's...5. in triangle abc, ab = ac = 15 cm and bc = 18 cm, find cos...
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![Page 1: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/1.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Exercise 22(A) Page:279
1. From the following figure, find the values of :
(i) sin A
(ii) cos A
(iii) cot A
(iv) sec C
(v) cosec C
(vi) tan C
Solution:
Given angle ABC = 900
AC = 5
(i)
(ii)
(iii)
(iv)
![Page 2: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/2.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(v)
(vi)
2. Form the following figure, find the values of :
(i) cos B
(ii) tan C
(iii) sin2B + cos2B
(iv) sin B. cos C + cos B. sin C
Solution:
Given angle BAC = 900
(i)
(ii)
(iii)
![Page 3: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/3.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(iv)
3. From the following figure, find the values of :
(i) cos A
(ii) cosec A
(iii) tan2A - sec2A
(iv) sin C
(v) sec C
(vi) cot2 C - π
πΊππππͺ
Solution:
![Page 4: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/4.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Given angle ADB and BDC = 900
(i)
(ii)
(iii)
(iv)
(v)
(vi)
![Page 5: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/5.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
4. From the following figure, find the values of :
(i) sin B
(ii) tan C
(iii) sec2 B - tan2B
(iv) sin2C + cos2C
Solution:
Given angle ADB=900 and ADC = 900
![Page 6: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/6.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
(iii)
(iv)
5. Given: sin A = 3/5 , find :
(i) tan A
(ii) cos A
Solution:
![Page 7: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/7.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
When length of BC=3x, length of AC = 5x
(i)
(ii)
6. From the following figure, find the values of :
(i) sin A
(ii) sec A
(iii) cos2 A + sin2A
Solution:
![Page 8: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/8.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
(iii)
7. Given: cos A = 5 / 13
Evaluate:
(i)
(ii)
Solution:
When length of AB = 5x, length of AC = 13x
![Page 9: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/9.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
8. Given: sec A = 29/21, evaluate : sin A β (1/tan A)
Solution:
When length of AB = 21x, length of AC = 29x
![Page 10: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/10.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
9. Given: tan A = 4/3, find:
Solution:
When the length of AB = 3x, length of BC = 4x
![Page 11: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/11.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
10. Given: 4 cot A = 3 find;
(i) sin A
(ii) sec A
(iii) cosec2 A - cot2A.
Solution:
When length of AB = 3x, length of BC = 4x
(i)
(ii)
(iii)
![Page 12: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/12.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
11. Given: cos A = 0.6; find all other trigonometrical ratios for angle A.
Solution:
When length of AB = 3x, length of AC = 5x
Now all other trigonometric ratios are
12. In a right-angled triangle, it is given that A is an acute angle and tan A = 5/12.
find the value of :
(i) cos A
(ii) sin A
![Page 13: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/13.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(iii) Solution:
When length of AB = 12x, length of BC = 5x
(i)
(ii)
(iii)
13. Given: sin π½ = p/q
Find cos π½ + sin π½ in terms of p and q.
Solution:
![Page 14: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/14.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
When length of perpendicular = px, length of hypotenuse = qx
14. If cos A = Β½ and sin B = 1/βπ, find the value of :
.
Are angles A and B from the same triangle? Explain.
Solution:
When length of AB = x, length of AC = 2x
![Page 15: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/15.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Therefore if length of AC = x, length of BC = β2π₯
15. If 5 cot π½= 12, find the value of : Cosec π½ + sec π½
Solution:
When length of base = 12x, length of perpendicular = 5x
![Page 16: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/16.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
16. If tan x = ππ
π , find the value of : 4 sin2x - 3 cos2x + 2
Solution:
When length of base = 3x, length of perpendicular = 4x
![Page 17: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/17.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
17. If cosec π½ = βπ, find the value of:
(i) 2 - sin2 - cos2
(ii)
Solution:
When length of hypotenuse = β5π₯, length of perpendicular = x
(i)
![Page 18: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/18.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(ii)
18. If sec A = βπ, find the value of :
Solution:
When length of AB = x, length of AC = β2π₯
![Page 19: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/19.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
19. If cot π½= 1; find the value of: 5 tan2π½+ 2 sin2 π½- 3
Solution:
When length of base = x, length of perpendicular = x
20. In the following figure:
AD BC, AC = 26 CD = 10, BC = 42,
DAC = x and B = y.
![Page 20: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/20.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Find the value of :
(i) cot x
(ii)
(iii)
Solution:
(i)
(ii)
![Page 21: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/21.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(iii)
![Page 22: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/22.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Exercise 22(B) Page:285
1. From the following figure, find:
(i) y
(ii) sin xo
(iii) (sec xo - tan xo) (sec xo + tan xo)
Solution:
(i)
Using Pythagorean Theorem
(ii)
(iii)
![Page 23: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/23.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
2. Use the given figure to find:
(i) sin xo
(ii) cos yo
(iii) 3 tan xo - 2 sin yo + 4 cos yo.
Solution:
Using Pythagorean Theorem
![Page 24: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/24.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
(iii)
3. In the diagram, given below, triangle ABC is right-angled at B and BD is perpendicular to AC.
Find:
(i) cos β DBC
(ii) cot β DBA
Solution:
![Page 25: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/25.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Using Pythagorean Theorem
In and , the is common to both the triangles,
.
Therefore and are similar triangles according to AAA Rule
So,
(i)
(ii)
4. In the given figure, triangle ABC is right-angled at B. D is the foot of the perpendicular from B to
AC. Given that BC = 3 cm and AB = 4 cm. find:
(i) tan DBC
(ii) sin DBA
![Page 26: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/26.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Solution:
Using Pythagorean Theorem
In and , the is common to both the triangles,
.
Therefore and are similar triangles according to AAA Rule
Using Pythagorean Theorem
![Page 27: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/27.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC.
Solution:
In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular drawn from angle A to
the side BC divides the side BC into two equal parts BD=DC=9cm
6. In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find:
(i) sin B
(ii) tan C
(iii) sin2 B + cos2B (iv) tan C - cot B
![Page 28: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/28.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Solution:
Since
(i)
(ii)
(iii)
![Page 29: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/29.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(iv)
7. In triangle ABC; ABC = 90o, CAB = xo, tan xo = ΒΎ and BC = 15 cm. Find the measures of AB
and AC.
Solution:
When length of base = 4x, length of perpendicular = 3x
![Page 30: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/30.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
8. Using the measurements given in the following figure:
(i) Find the value of sin and tan .
(ii) Write an expression for AD in terms of
Solution:
Draw a perpendicular from D to side AB at point E which makes BCDE is a rectangle.
From triangle BCD, using Pythagorean Theorem
Since BCDE is rectangle so ED 12 cm, EB = 5 and AE = 14 - 5 = 9
(i)
(ii)
![Page 31: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/31.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Or
9. In the given figure;
BC = 15 cm and sin B = 4/5
(i) Calculate the measure of AB and AC.
(ii) Now, if tan ADC = 1; calculate the measures of CD and AD.
Also, show that: tan2B β 1/ cos2B = -1
Solution:
Given
When length of perpendicular = 4x, length of hypotenuse = 5x
![Page 32: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/32.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
Given
When length of perpendicular = x, length of hypotenuse = x
![Page 33: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/33.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
10. If sin A + cosec A = 2;
Find the value of sin2 A + cosec2 A.
Solution:
Squaring both sides
11. If tan A + cot A = 5;
Find the value of tan2 A + cot2 A.
Solution:
Squaring both sides
12. Given: 4 sin = 3 cos ; find the value of:
(i) sin π½
(ii) cos π½
(iii) cot2 π½ - cosec2 π½.
(iv) 4 cos2 π½ - 3 sin2 π½ + 2
Solution:
![Page 34: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/34.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
When length of BC = 3x, length of AB = 4x
(i)
(ii)
(iii)
(iv)
![Page 35: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/35.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
13. Given : 17 cos π½ = 15;
Find the value of: tan π½ + 2 sec π½.
Solution:
When length of AB = 15x, length of AC = 17x
14. Given : 5 cos A - 12 sin A = 0; evaluate :
.
Solution:
![Page 36: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/36.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
15. In the given figure; C = 90o and D is mid-point of AC. Find
(i) (ii)
Solution:
Since is mid-point of so
(i)
![Page 37: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/37.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(ii)
16. If 3 cos A = 4 sin A, find the value of :
(i) cos A
(ii) 3 - cot2 A + cosec2A.
Solution:
Therefore if length of AB = 4x, length of BC = 3x
Since
(i)
![Page 38: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/38.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(ii)
17. In triangle ABC, B = 90o and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.
Solution:
When length of base = 4x, length of perpendicular = 3x
![Page 39: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/39.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
18. In rhombus ABCD, diagonals AC and BD intersect each other at point O.
If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the the side and the diagonals of
the rhombus.
Solution:
When length of base = 3x, length of hypotenuse = 5x
![Page 40: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/40.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
The sides of a rhombus are equal.
So, the length of the side of the rhombus = 10cm
The diagonals are
19. In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find:
(i) cos B
(ii) sin C
(iii) tan2 B - sec2 B + 2
Solution:
In the isosceles triangle ABC, the perpendicular drawn from angle A to the side BC divides the side BC into
two equal parts BD = DC = 9cm
Since
(i)
(ii)
(iii)
![Page 41: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/41.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
20. In triangle ABC, AD is perpendicular to BC. sin B = 0.8, BD = 9 cm and tan C = 1. Find the length
of AB, AD, AC and DC.
Solution:
When length of perpendicular = 4x, length of hypotenuse = 5x
![Page 42: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/42.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
if length of perpendicular = x, length of base = x
21. Given q tan A = p, find the value of :
.
Solution:
![Page 43: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/43.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
22. If sin A = cos A, find the value of 2 tan2A - 2 sec2 A + 5.
Solution:
If length of perpendicular = x, length of base = x
![Page 44: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/44.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
23. In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the
perimeter of the rectangle ABCD.
Solution:
If length of base = 3x, length of perpendicular = 2x
![Page 45: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/45.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
24. If 2 sin x = , evaluate.
(i) 4 sin3 x - 3 sin x.
(ii) 3 cos x - 4 cos3 x.
Solution:
![Page 46: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/46.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(i)
(ii)
25. If sin A = and cos B = , find the value of : .
Solution:
![Page 47: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/47.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
![Page 48: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/48.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
26. Use the informations given in the following figure to evaluate:
Solution:
Using Pythagorean Theorem
Using Pythagorean Theorem
![Page 49: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/49.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Then,
27. If sec A = βπ,
find: .
Solution:
![Page 50: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/50.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
Then,
28. If 5 cos π½ = 3,
evaluate : .
Solution:
![Page 51: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/51.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
29. If cosec A + sin A = 5π
π, find the value of cosec2A + sin2A.
Solution:
Squaring both sides
30. If 5 cos π½ = 6 sin π½ ; evaluate:
(i) tan π½
![Page 52: Exercise 22(A) Page:279 - Byju's...5. In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC. Solution: In the isosceles triangle ABC, AB = AC = 15 cm and BC = 18cm the perpendicular](https://reader035.vdocuments.mx/reader035/viewer/2022070223/613df8dd59df642846163b28/html5/thumbnails/52.jpg)
Concise Selina Solutions for Class 9 Maths Chapter 22-
Trigonometrical Ratios
(ii)
Solution:
(i)
(ii)