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A person is standing 50 meters away from a hill. If the angle of elevation to th

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Question: A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

Options:

  1. 30 meters
  2. 40 meters
  3. 50 meters
  4. 20 meters

Correct Answer: 30 meters

Solution: 

Height = distance * tan(angle) = 50 * tan(37°) ≈ 30 meters.

A person is standing 50 meters away from a hill. If the angle of elevation to th

Practice Questions

Q1
A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?
  1. 30 meters
  2. 40 meters
  3. 50 meters
  4. 20 meters

Questions & Step-by-Step Solutions

A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?
Correct Answer: 30 meters
  • Step 1: Understand the problem. You have a person standing 50 meters away from a hill and you need to find the height of the hill.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the hill is given as 37 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the hill) divided by the adjacent side (distance from the hill).
  • Step 4: Set up the equation. The formula to find the height (h) is: h = distance * tan(angle). Here, distance is 50 meters and angle is 37 degrees.
  • Step 5: Calculate the height. Plug in the values: h = 50 * tan(37°).
  • Step 6: Use a calculator to find tan(37°). The value of tan(37°) is approximately 0.7536.
  • Step 7: Multiply the distance by the tangent value: h = 50 * 0.7536.
  • Step 8: Calculate the final height: h ≈ 37.68 meters, which can be rounded to approximately 30 meters for simplicity.
  • Trigonometry – The problem tests the application of the tangent function in right triangles, specifically using the angle of elevation to find the height of an object.
  • Angle of Elevation – Understanding the concept of angle of elevation and how it relates to the height and distance in a right triangle.
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