Chapter 10 - NCPN

Finding Angle Measures
Inverse trigonometric functions can be used to find missing angle measures
when you know the side lengths of a right triangle.
Example 2
Finding an Angle Measure
Given Side Lengths
Use the information from the opening paragraph of this lesson. What is the
measure, in degrees, of the angle of the ramp’s incline Round your answer
to the nearest tenth.
Solution
Draw a diagram.
Recall that the tangent of an angle in a right triangle is defined as the ratio of
the length of the side opposite the angle to the length of the side adjacent to
the angle. So, tan x = 2 . Use the inverse tangent function to solve for x.
5
tan x =
2
5
tan (tan x)
= tan
x ≈ 21.
8°
2
5
−1 − 1( )
The angle of the ramp’s incline, rounded to the nearest tenth, is 21.8°.
Ongoing Assessment
The figure shows the cross-section of a roof. What is the roof’s angle of
incline, x, in degrees Round your answer to the nearest tenth. 22.6°
450 Chapter 10 Trigonometric Functions and Identities