This document defines the angle of depression as the angle below the horizontal that an observer looks to see an object lower than them, and defines the angle of elevation as the angle above the horizontal an observer looks to see a higher object. It provides two examples using trigonometry: one calculating the height of a tree using a 51 degree angle of elevation, and another calculating the distance to a boat using a 10 degree angle of depression.

1.  8-7 Applications of RightTriangle
Trigonometry
Objective:
1. I can distinguish between the angle of
depression and the angle of elevation.

2.  Definition:The angle of depression is the angle below the
horizontal line that an observer must look in order to see an
object that is lower than the observer

5.  Definition:The angle of elevation is the angle above the
horizontal line that an observer must look in order to see an
object that is higher than the observer

9.  Example 1

10. tan 51 =
ℎ
21
21 ∙ tan 51 = ℎ
21 ∙ 1.2349 = ℎ
26 ≈ ℎ
The tree is about 26 ft. tall.

11.  Example 2

12. tan 10 =
25
𝑥
𝑥 =
25
tan 10
𝑥 ≈ 142
The boat is about 142 m from the base of the lighthouse.