geometry chapter 7. this slideshow was developed to accompany the textbook larson geometry by...
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![Page 1: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/1.jpg)
Right Triangle TrigonometryGeometry Chapter 7
![Page 2: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/2.jpg)
This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff,
L. 2011 Holt McDougal
Some examples and diagrams are taken from the textbook.
Slides created by Richard Wright, Andrews Academy [email protected]
![Page 3: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/3.jpg)
Find the value of x
7.1 Apply the Pythagorean Theorem
Pythagorean TheoremIn a right triangle, a2 + b2 = c2 where a and b are the length of the legs and c is the length of the hypotenuse.
![Page 4: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/4.jpg)
The top of a ladder rests against a wall, 23 ft above the ground. The base of the ladder is 6 ft away from the wall. What is the length of the ladder.
7.1 Apply the Pythagorean Theorem
![Page 5: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/5.jpg)
Find the area of the triangle
7.1 Apply the Pythagorean Theorem
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Pythagorean Triples A set of three positive integers that
satisfy the Pythagorean Theorem
7.1 Apply the Pythagorean Theorem
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Use a Pythagorean Triple to solve
436 #4-34 even, 40-50 even = 22
7.1 Apply the Pythagorean Theorem
![Page 8: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/8.jpg)
7.1 Answers
7.1 Homework Quiz
Answers and Quiz
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Tell whether a triangle with the given sides is a right triangle.
7.2 Use the Converse of the Pythagorean Theorem
Converse of the Pythagorean TheoremIf a2 + b2 = c2 where a and b are the length of the short sides and c is the length of the longest side, then it is a right triangle.
![Page 10: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/10.jpg)
Show that the segments with lengths 3, 4, and 6 can form a triangle
Classify the triangle as acute, right or obtuse.
444 #2-30 even, 33, 38, 40, 44-52 even = 23 Extra Credit 447 #2, 8 = +2
7.2 Use the Converse of the Pythagorean Theorem
If c is the longest side and…c2 < a2 + b2 acute trianglec2 = a2 + b2 right trianglec2 > a2 + b2 obtuse triangle
![Page 11: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/11.jpg)
7.2 Answers
7.2 Homework Quiz
Answers and Quiz
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ΔCBD ~ ΔABC, ΔACD ~ ΔABC, ΔCBD ~ ΔACD
7.3 Use Similar Right TrianglesIf the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
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Identify the similar triangles. Then find x.E
FG
3
4
5
7.3 Use Similar Right Triangles
E
FG
H
3
4
x
5
FG
H
4
x
E
G
H
3x
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7.3 Use Similar Right TrianglesIf the altitude is drawn to the hypotenuse of a right triangle, then the altitude is the geometric mean of the two segments of the hypotenuse.
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7.3 Use Similar Right TrianglesIf the altitude is drawn to the hypotenuse of a right triangle, then each leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to that leg.
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Find the value of x or y.
453 #4-26 even, 30-34 even, 40-48 even = 20
7.3 Use Similar Right Triangles
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7.3 Answers
7.3 Homework Quiz
Answers and Quiz
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7.4 Special Right Triangles
Some triangles have special lengths of sides, thus in life you see these triangles often such as in construction.
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7.4 Special Right Triangles
45-45-90 If you have another 45-45-90 triangle,
then use the fact that they are similar and use the proportional sides.
The leg of one 45-45-90 triangle is 10. Find the lengths of the other sides. 1
1
√245°
45°
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7.4 Special Right Triangles30-60-90
The hypotenuse of a 30-60-90 is 4. Find the lengths of the other sides.
461 #2-20 even, 24, 28, 30, 36-38 all, 40, 42-44 all = 20
Extra Credit 464 #2, 4 = +2
√3
2130°
60°
![Page 21: Geometry Chapter 7. This Slideshow was developed to accompany the textbook Larson Geometry By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L](https://reader030.vdocuments.mx/reader030/viewer/2022013115/56649cc15503460f949886c0/html5/thumbnails/21.jpg)
7.4 Answers
7.4 Homework Quiz
Answers and Quiz
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Draw a large 30° angle. On one side, draw a perpendicular lines every 5 cm. Fill in the table
Why are and ?
7.5 Apply the Tangent Ratio
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Tangent ratio
7.5 Apply the Tangent Ratio
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Find tan J and tan K.
7.5 Apply the Tangent Ratio
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Find the value of x. Round to the nearest tenth.
469 #4-28 even, 32, 36-46 even = 20
7.5 Apply the Tangent Ratio
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7.5 Answers
7.5 Homework Quiz
Answers and Quiz
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7.6 Apply the Sine and Cosine Ratios
S O HC A HT O A
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Find sin X, cos X, and tan X
7.6 Apply the Sine and Cosine Ratios
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Find the length of the dog run (x).
7.6 Apply the Sine and Cosine Ratios
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Angle of Elevation and Depression Both are measured from the
horizontal Since they are measured to || lines,
they are =̃E
7.6 Apply the Sine and Cosine Ratios
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The angle of elevation of a plane as seen from the airport is 50°. If the plane’s 1000 ft away, how high is plane?
477 #2-30 even, 34, 36, 42-48 even = 21
7.6 Apply the Sine and Cosine Ratios
50°
x 1000 ft
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7.6 Answers
7.6 Homework Quiz
Answers and Quiz
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Solve a triangle means to find all the unknown angles and sides. Can be done for a right triangle if you know
2 sides 1 side and 1 acute angle
Use sin, cos, tan, Pythagorean Theorem, and Angle Sum Theorem
7.7 Solve Right Triangles
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Inverse Trigonometric Ratios Used to find measures of angles
when you know the sides.
7.7 Solve Right Triangles
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Find to the nearest tenth if
Find to the nearest tenth.
7.7 Solve Right Triangles
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Solve a right triangle that has a 40° angle and a 20 inch hypotenuse.
485 #2-28 even, 32-38 even, 43, 44-48 even = 22 Extra Credit 489 #2, 4 = +2
7.7 Solve Right Triangles
20
40°
A C
B
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7.7 Answers
7.7 Homework Quiz
Answers and Quiz
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Tangent, Sine, and Cosine are only for right triangles
Law of Sines and Law of Cosines are for any triangle
7.Extension Law of Sines and Law of Cosines
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Law of Sines
Used if you know AAS, ASA, SSA
7.Extension Law of Sines and Law of Cosines
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How much closer to school does Jimmy live than Adolph?
7.Extension Law of Sines and Law of Cosines
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Law of Cosines
Use when you know SSS, SAS
7.Extension Law of Sines and Law of Cosines
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Find f to the nearest hundredth.
491 #1-7 =̃ 7
7.Extension Law of Sines and Law of Cosines
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7.Extension Answers
Answers
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498 #1-17 = 17
7.Review