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\(\textbf{1)}\) You are standing 10 feet from the base of a tree. You look up at the top of the tree with an angle of elevation of 60 degrees. How tall is the tree?
\(\textbf{2)}\) You are in a hot air balloon. You look at Steve with an angle of depression of 30 degrees. Your elevation is 1200 feet. How far apart are you and Steve?
\(\textbf{3)}\) You are flying a kite. You let out 40 feet of string at an angle of elevation of 40 degrees. How high up is the kite?
\(\textbf{4)}\) You are on top of a building. You look down on the neighboring building at an angle of depression of 30 degrees. Your building is 100 feet tall. The buildings are 30 feet apart. How tall is the other building?
\(\textbf{5)}\) From the top of a lighthouse, the angle of depression to a boat is 45 degrees. If the lighthouse is 100 feet tall, how far is the boat from the base of the lighthouse?
\(\textbf{6)}\) You are flying a kite and hold the string 80 feet long. The angle of elevation to the kite is 50 degrees. How high is the kite above the ground?
\(\textbf{7)}\) A person looks up at the top of a cliff with an angle of elevation of 20 degrees. If they are standing 200 feet away from the base of the cliff, how tall is the cliff?
\(\textbf{8)}\) From the top of a building, the angle of depression to a car on the street is 40 degrees. If the building is 80 feet tall, how far is the car from the base of the building?
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\(\bullet\text{ Angle of Depression and Elevation}\)
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In Summary
Word problems in trigonometry often involve finding the angle of depression or elevation. These angles are formed between a horizontal line of sight and a line of sight downward or upward, respectively.
Word problems involving angle of depression and elevation are typically covered in high school trigonometry or precalculus classes. We learn about these because it provides a practical application for the concepts learned in this branch of mathematics. These types of problems can be found in fields such as surveying, meteorology, and navigation.
Common mistakes when solving word problems involving angle of depression and elevation is not understanding which angle is the angle of depression. It is usually not the upper angle in the triangle drawing for the problem. It is the angle off of the horizontal line. Usually the angle of depression is equal to the angle of elevation, which is usually the bottom acute angle in the drawing.
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