Download Find m J for each right triangle to the nearest degree. 36. ANSWER

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10-6 Trigonometric Ratios
Find m
J for each right triangle to the nearest degree.
36. ANSWER: 25°
37. ANSWER: 62°
38. ANSWER: 59°
39. ANSWER: 31°
40. ANSWER: 72°
41. eSolutions Manual - Powered by Cognero
ANSWER: 50°
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40. 10-6ANSWER: Trigonometric Ratios
72°
41. ANSWER: 50°
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?
ANSWER: about 69 ft
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.
ANSWER: 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?
ANSWER: about 60°
Suppose
A is an acute angle of right triangle ABC .
45. Find sin A and tan A if cos
.
ANSWER: 46. Find tan A and cos A if sin
.
ANSWER: 47. Find cos A and tan A if sin
.
ANSWER: 48. Find sin A and cos A if tan
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ANSWER: .
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ANSWER: 10-6 Trigonometric Ratios
48. Find sin A and cos A if tan
.
ANSWER: 49. SUBMARINES A submarine descends into the ocean at an angle of 10° below the water line and travels 3 miles diagonally. How far beneath the surface of the water has the submarine reached?
ANSWER: about 0.5 mi
50. MULTIPLE REPRESENTATIONS In this problem, you will explore a relationship between the sine and cosine
functions.
a. TABULAR Copy and complete the table using the triangles shown above.
b. VERBAL Make a conjecture about the sum of the squares of the sine and cosine of an acute angle of an acute
angle in a right triangle.
ANSWER: a.
Triangle
2
Trigonometric Ratios
2
sin
2
sin A =
cos A =
sin A =
sin C =
cos C =
sin C =
sin J =
cos J =
sin J =
sin L =
cos L =
sin L =
sin X =
cos X =
sin X =
sin Z =
cos Z =
sin Z =
cos
2
cos A =
2
ABC
2
2
2
1
2
1
2
1
2
1
2
1
cos C =
cos J =
JKL
2
2
cos L =
cos X =
XYZ
2
2
sin + cos =
1
cos Z =
b. The sum of the squares of the sine and cosine of an acute angle in a right triangle is equal to 1.
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