# Angles of Elevation & Depression: Practice Problems

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Frequency & Relative Frequency Tables: Definition & Examples

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:03 Definitions of Angles
• 0:38 Practice Problem #1
• 1:52 Practice Problem #2
• 3:06 Practice Problem #3
• 4:03 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay

#### Recommended Lessons and Courses for You

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:

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

To unlock this lesson you must be a Study.com Member.

### Register for a free trial

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it free for 5 days!

Support