Angles of Elevation & Depression: Practice Problems

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  • 0:03 Definitions of Angles
  • 0:38 Practice Problem #1
  • 1:52 Practice Problem #2
  • 3:06 Practice Problem #3
  • 4:03 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Angles of elevation and depression can be used to find unknown heights and distances. In this lesson, you can practice using angles of elevation and depression to solve problems.

Definitions of Angles

Imagine you're walking through a forest and look up at the top of a tall tree. The angle between the horizontal ground and your line of sight to the top of the object (the tree in this case) is known as the angle of elevation. Similarly, if you're looking down at something below you, the angle of depression is measured between the horizontal and your line of sight downward to the object.

You can use angles of depression and elevation, along with the trigonometric functions sine, cosine, and tangent, to calculate unknown distances. Let's look at three practice problems that will help you understand how to do this.

Practice Problem #1

There's a tall tree in your backyard and you think it might hit your house if it fell over. You measure that the base of the tree is 48 feet from your house, but you don't know how tall the tree is. To determine the height of the tree, you stand just outside your back door and measure the angle of elevation from the ground to the tree to be 64 degrees. How tall is the tree?

To figure this out, first carefully draw a picture of the situation and label all the distances and angles that you know. In this case, you know the distance to the base of the tree (48 ft) and the angle of elevation from the ground to the tree (64 degrees).

Then you will use one or more of the trig functions to find the missing side of the triangle (the height of the tree, h). Here, since you know the angle and the adjacent side and you want to find the opposite side of the triangle, you will want to use the tangent function:


example1


So you now know that the tree is 98 ft tall. Would it fall on your house or not? Probably, yes! If the tree fell toward your house, it would certainly hit because the tree is 98 ft tall and there are only 48 ft from your house to the base of the tree.

Practice Problem #2

Standing on a 35 meter high cliff, you look down on your friend who is standing on the flat ground in front of the cliff. The angle of depression along the line of sight from you to your friend is 65 degrees. How far away from the cliff is your friend?

First, notice that to find the angle inside the triangle, you will need to subtract the angle of depression from 90 degrees.

90 degrees - 65 degrees = 25 degrees

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