CK-12 Geometry - Second Edition

8.6. Inverse Trigonometric Ratios http://www.ck12.org

Solution:First, draw a picture. The angle that the sun hits the flagpole is the acute angle at the top of the triangle,
x◦. From the picture, we can see that we need to use the inverse tangent ratio.

tanx=

42

25

tan−^1

42

25

≈ 59. 2 ◦=x

Example 7:Elise is standing on the top of a 50 foot building and spots her friend, Molly across the street. If Molly
is 35 feet away from the base of the building, what is the angle of depression from Elise to Molly? Elise’s eye height
is 4.5 feet.

Solution:Because of parallel lines, the angle of depression is equal to the angle at Molly, orx◦. We can use the
inverse tangent ratio.

tan−^1

(

54. 5

30

)

= 61. 2 ◦=x

Know What? RevisitedTo find the escalator’s angle of elevation, we need to use the inverse sine ratio.

sin−^1

(

115

230

)

= 30 ◦ The angle of elevation is 30◦.

Review Questions

Use your calculator to findm^6 Ato the nearest tenth of a degree.

1.