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Angle of Elevation and Depression


Videos, worksheets, solutions, and activities to help students learn how to find the angle of elevation and depression using trigonometry.

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Angle of Elevation and Depression : In real world situations we often discuss the angle of elevation and depression. The angle of elevation and depression is used often in word problems, especially those involving a persons line of sight as they look up at an object.
This video will explain what is the angle of elevation and what is the angle of depression.
It will also give some examples of how to use the angles of elevation and angles of depression.
Angle of Elevation/Depression Story Problems
Example: The angle of elevation from point A to the top of a cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how high is the cliff? Let x be the height of the cliff.
1. From the top of the tower, the angle of depression to a stake on the ground is 72 degress. The top of the tower is 80 feet above the ground. How far is the stake from the foot of the tower?
2. A tree 40 feet high casts a shadow 58 feet long. Find the measure of elevation of the sun.
3. A ladder leaning against a house makes an angle of 60 degrees with the ground. The foot of the ladder is 7 feet from the foundation of the house. How long is the ladder?
4. A balloon on a 40-foot string makes an angle of 50 degrees with the ground. How high above the ground is the balloon if the hand of the person holding the balloon is 6 feet above the ground?

Angles of Elevation and Depression
This video goes through three word problems that require trigonometry to calculate side lengths or angle measures in right triangles.
1. A salvage ship uses sonar to determine that the angle of depression to the wreck on the ocean floor is 13.25 degrees. The depth chart shows that the ocean floor is 40 meters below the surface. How far must the diver lowered from the salvage ship walk along the ocean floor to reach the wreck?
2. Find the angle of elevation of the sun when a 7.6 m flag pole casts a 18.2 m shadow.
3. Olivia is in a lighthouse on a cliff. The top of the cliff is 110 feet above the water and Olivia is in a place in the lighthouse 85 feet above the top of the cliff. She observes two sailboats due east of the lighthouse. The angle of depression to the two boats are 33 degrees and 57 degrees. Find the distance between the two boats.
Determining the Angle of Elevation
How to determine the angle of elevation.

Angle of elevation part 1
The passengers on a ship, 3700 m from the base of a 1800 m high cliff are able to see the Byron Bay lighthouse on top of a cliff. Find the angle of elevation from the ship to the top of the cliff.
Angle of elevation part 2

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