10-6 Trigonometric Ratios
Solve each right triangle. Round each side length to the nearest tenth.
32. SOLUTION: Find the measure of
.
Find
.
Find
.
33. SOLUTION: Find the measure of
.
Find
.
Find
.
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10-6 Trigonometric Ratios
33. SOLUTION: Find the measure of
.
Find
.
Find
.
34. SOLUTION: Find the measure of
.
Find
.
Find
.
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35. ESCALATORS At a local mall, an escalator is 110 feet long. The angle the escalator makes with the ground is
29°. Find the height reached by the escalator.
10-6 Trigonometric Ratios
34. SOLUTION: Find the measure of
.
Find
.
Find
.
35. ESCALATORS At a local mall, an escalator is 110 feet long. The angle the escalator makes with the ground is
29°. Find the height reached by the escalator.
SOLUTION: The escalator is about 53 ft high.
Find m
J for each right triangle to the nearest degree.
36. SOLUTION: You know the measure of the side opposite ∠J and the measure of the hypotenuse. Use the sine ratio.
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Use a calculator and the [sin ]function to find the measure of the angle.
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10-6 Trigonometric Ratios
The escalator is about 53 ft high.
Find m
J for each right triangle to the nearest degree.
36. SOLUTION: You know the measure of the side opposite ∠J and the measure of the hypotenuse. Use the sine ratio.
–1
Use a calculator and the [sin ]function to find the measure of the angle.
Keystrokes:
So, m∠J ≈ 25°.
-1
[SIN ] 10
24
24.62431835
37. SOLUTION: You know the measure of the side opposite ∠J and the measure of the hypotenuse. Use the sine ratio.
–1
Use a calculator and the [sin ] function to find the measure of the angle.
Keystrokes:
So, m∠J ≈ 62°.
-1
[SIN ] 15
17
61.92751306
38. SOLUTION: You know the measure of the side opposite ∠J and the measure of the side adjacent to ∠J. Use the tangent ratio.
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–1
Keystrokes:
[SIN ] 15
So, m∠J ≈ 62°.
10-6 Trigonometric Ratios
17
61.92751306
38. SOLUTION: You know the measure of the side opposite ∠J and the measure of the side adjacent to ∠J. Use the tangent ratio.
–1
Use a calculator and the [tan ] function to find the measure of the angle.
Keystrokes:
So, m∠J ≈ 59°.
-1
[TAN ] 23
14
58.67130713
39. SOLUTION: You know the measure of the side opposite ∠J and the measure of the side adjacent to ∠J. Use the tangent ratio.
–1
Use a calculator and the [tan ] function to find the measure of the angle.
Keystrokes:
-1
[TAN ] 6
10
30.96375653
So, m∠J ≈ 31°.
40. SOLUTION: You know the measure of the side adjacent to ∠J and the measure of the hypotenuse. Use the cosine ratio.
–1
Use a calculator and the [cos ] function to find the measure of the angle.
Keystrokes:
-1
[COS ] 5
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So, m∠J ≈ 72°.
16
71.79004314
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Keystrokes:
-1
[TAN ] 6
30.96375653
10
m∠J ≈ 31°. Ratios
10-6So,
Trigonometric
40. SOLUTION: You know the measure of the side adjacent to ∠J and the measure of the hypotenuse. Use the cosine ratio.
–1
Use a calculator and the [cos ] function to find the measure of the angle.
Keystrokes:
-1
[COS ] 5
16
71.79004314
So, m∠J ≈ 72°.
41. SOLUTION: You know the measure of the side adjacent to ∠J and the measure of the hypotenuse. Use the cosine ratio.
–1
Use a calculator and the [cos ] function to find the measure of the angle.
Keystrokes:
So, m∠J ≈ 50°.
-1
[COS ] 11
17 49.67978493
42. MONUMENTS The Lincoln Memorial building measures 204 feet long, 134 feet wide, and 99 feet tall. Chloe is
looking at the top of the monument at an angle of 55°. How far away is she standing from the monument?
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-1
Keystrokes:
[COS ] 11
m∠J ≈ 50°. Ratios
10-6So,
Trigonometric
17 49.67978493
42. MONUMENTS The Lincoln Memorial building measures 204 feet long, 134 feet wide, and 99 feet tall. Chloe is
looking at the top of the monument at an angle of 55°. How far away is she standing from the monument?
SOLUTION: Chloe is standing about 69 ft away from the monument.
43. AIRPLANES Ella looks down at a city from an airplane window. The airplane is 5000 feet in the air, and she looks
down at an angle of 8°. Determine the horizontal distance to the city.
SOLUTION: The horizontal distance to the city is about 35,577 ft.
44. FORESTS A forest ranger estimates the height of a tree is about 175 feet. If the forest ranger is standing 100 feet
from the base of the tree, what is the measure of the angle formed between the range and the top of the tree?
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10-6 Trigonometric Ratios
The horizontal distance to the city is about 35,577 ft.
44. FORESTS A forest ranger estimates the height of a tree is about 175 feet. If the forest ranger is standing 100 feet
from the base of the tree, what is the measure of the angle formed between the range and the top of the tree?
SOLUTION: The angle formed between the ground and the top of the tree is about 60°.
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