Problem-Solving with Angles of Elevation & Depression


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question 1 of 3

Ski Lift Corp wants to build a ski lift at a 30-degree angle of elevation up to the very peak of a mountain, as shown in the picture. If the mountain is 4,000 feet tall, how long should the cable for the ski lift be?

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When Caesar surveys his conquering legions, he stands on a cliff face 2,000 feet above the level of the plain where the army is assembled. Being a mathematically-minded Roman, Caesar has measured the angle of depression of his gaze, and determined that it is 20 degrees (Caesar's gaze is shown in orange in the picture). Approximately how far away, in feet, is Caesar's army from the base of the cliff (namely, how long is the green line in the picture)?

It's fine to round all decimals in your work and your answer to 2 decimal places.

2. An airplane takes off at an angle of elevation of 15 degrees. Approximately many feet in total will it fly before it reaches its cruising altitude of 10,000 feet and you finally get your package of peanuts?

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About This Quiz & Worksheet

This short quiz/worksheet assessment is a great tool if you're looking to quickly determine how much you know about angles of elevation and depression. You must be able to apply what you know to solving sample problems relating to these angles in order to complete this brief quiz.

Quiz & Worksheet Goals

The quiz will test your ability to do the following:

  • Solve sample angles of elevation and depression problems
  • Understand angles of elevation and depression
  • Apply your knowledge of angles of elevation and depression

Skills Practiced

  • Critical thinking - apply relevant concepts to examine information about angles of elevation and depression in a different light
  • Problem solving - use acquired knowledge to solve angles of elevation and depression practice problems
  • Interpreting information - verify that you can read information regarding elevation and depression and interpret it correctly

Additional Learning

More details can be reviewed in the lesson called Problem-Solving with Angles of Elevation & Depression. You will be able to learn more about:

  • How angle of elevation and angle of depression are defined
  • What SOH-CAH-TOA refers to
  • What real-world problems can be solved using knowledge of angles of elevation and depression