right angle trigonometry. labeling a right triangle in trigonometry, we give each side a name...
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Right Angle Trigonometry
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Labeling a Right Triangle In trigonometry, we give each side a
name according to its position in relation to any given angle in the triangle: Hypotenuse, Opposite, Adjacent
Hypotenuse
Ad
jace
nt
Opposite
The _________ is always the longest side of the triangle.
The _________ side is the leg directly across from the angle. The _________ side is the leg alongside the angle.
hypotenuse
opposite
adjacent
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Trigonometric RatiosWe define the 3
trigonometric ratios in terms of fractions
of sides of right angled triangles.
Hypotenuse
(HYP)
Ad
jace
nt
(AD
J)
Opposite (OPP)
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SohCahToaSine equals Opposite over HypotenuseCosine equals Adjacent over HypotenuseTangent equals Opposite over Adjacent
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Practice Together:Given each triangle, write the ratio that could be used to find x by connecting the angle and sides given.
65 a
x
Find x.
32
bx
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YOU DO:Given the triangle, write all the ratios that could be used to find x by connecting the angle and sides given.
56
d
x
Find x.
c
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In a right triangle, if we are given another angle and a side we can
find:
The third angle of the right triangle: How?
The other sides of the right triangle: How?
Using the ‘angle sum of a triangle is 180’
Using the trig ratios
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Steps to finding the missing sides of a right triangle using trigonometric ratios:
1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle
61 9.6 cm
x
HYP
OPP
ADJ
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Steps to finding the missing sides of a right triangle using trigonometric ratios:
2. For the given angle choose the correct trigonometric ratio which can be used to set up an equation
3. Set up the equation
61 9.6 cm
x
HYP
OPP
ADJ
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Steps to finding the missing sides of a right triangle using trigonometric ratios:
4. Solve the equation to find the unknown.61
9.6 cm
x
HYP
OPP
ADJ
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Practice Together:Find, to 2 decimal places, the unknown length in the triangle.
41
x m7.8 m
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YOU DO:Find, to 1 decimal place, all the unknown angles and sides in the triangle.
a m
14.6 m
63
b m
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Steps to finding the missing angle of a right triangle using trigonometric ratios:
1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle
5.92 kmHYP
OPP
ADJ
2.6
7
km
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Steps to finding the missing angle of a right triangle using trigonometric ratios:
2. For the unknown angle choose the correct trig ratio which can be used to set up an equation
3. Set up the equation
5.92 kmHYP
OPP
ADJ
2.6
7
km
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Steps to finding the missing angle of a right triangle using trigonometric ratios:
4. Solve the equation to find the unknown using the inverse of trigonometric ratio.
5.92 kmHYP
OPP
ADJ
2.6
7
km
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Practice Together:Find, to one decimal place, the unknown angle in the triangle.
3.1 km 2.1
km
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YOU DO:Find, to 1 decimal place, the unknown angle in the given triangle.
7 m
4 m
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Practice: Isosceles Triangles Using what we already know about right
angles in isosceles triangles find the unknown side.
10 cm
x cm
67
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YOU DO: Isosceles Triangles Find the unknown angle of the isosceles
triangle using what you already know about right angles in isosceles triangles.
8.3 m
5.2 m
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Practice: Circle Problems Use what you already know about right
angles in circle problems to find the unknown angle.
6 cm
10 cm
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YOU DO: Circle Problems Use what you already know about right
angles in circle problems to find the unknown side length.
6.5 cm
56
x cm
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Practice: Other Figures (Trapezoid) Find x given:
10 c
m
x cm
65 48
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YOU DO: Other Figures (Rhombus) A rhombus has diagonals of length 10
cm and 6 cm respectively. Find the smaller angle of the rhombus.
10
cm
6 cm