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A person is standing 25 meters away from a hill. If the angle of elevation to th

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Question: A person is standing 25 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. 15 meters
  2. 20 meters
  3. 25 meters
  4. 30 meters

Correct Answer: 20 meters

Solution: 

Height = distance * tan(37) = 25 * 0.7536 ≈ 18.84 meters, rounded to 20 meters.

A person is standing 25 meters away from a hill. If the angle of elevation to th

Practice Questions

Q1
A person is standing 25 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. 15 meters
  2. 20 meters
  3. 25 meters
  4. 30 meters

Questions & Step-by-Step Solutions

A person is standing 25 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: 20 meters
  • Step 1: Understand the problem. You have a person standing 25 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 height of the hill can be calculated using the formula: Height = distance * tan(angle).
  • Step 5: Plug in the values. Here, distance = 25 meters and angle = 37 degrees. So, Height = 25 * tan(37).
  • Step 6: Calculate tan(37 degrees). The value of tan(37 degrees) is approximately 0.7536.
  • Step 7: Multiply the distance by the tangent value. Height = 25 * 0.7536.
  • Step 8: Perform the multiplication. Height ≈ 18.84 meters.
  • Step 9: Round the answer. The height of the hill is approximately 20 meters when rounded.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the hill.
  • Angle of Elevation – Understanding how the angle of elevation is used to calculate the height of an object based on a horizontal distance.
  • Rounding – The importance of rounding the final answer correctly based on significant figures or context.
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