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

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Question: A person is standing 25 meters away from a wall. If the angle of elevation to the top of the wall is 75 degrees, what is the height of the wall?

Options:

  1. 24.5 meters
  2. 25 meters
  3. 26.5 meters
  4. 27.5 meters

Correct Answer: 27.5 meters

Solution: 

Height = distance * tan(75) = 25 * 3.732 = 93.3 meters.

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

Practice Questions

Q1
A person is standing 25 meters away from a wall. If the angle of elevation to the top of the wall is 75 degrees, what is the height of the wall?
  1. 24.5 meters
  2. 25 meters
  3. 26.5 meters
  4. 27.5 meters

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a wall. If the angle of elevation to the top of the wall is 75 degrees, what is the height of the wall?
Correct Answer: 93.3 meters
  • Step 1: Understand the problem. You have a person standing 25 meters away from a wall and looking up at the top of the wall at an angle of 75 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the wall, the other side is the distance from the person to the wall (25 meters), and the angle between the ground and the line of sight to the top of the wall is 75 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 wall) divided by the adjacent side (distance to the wall). So, tan(75 degrees) = height / 25 meters.
  • Step 4: Rearrange the formula to find the height. Height = distance * tan(75 degrees).
  • Step 5: Calculate tan(75 degrees). You can use a calculator to find that tan(75 degrees) is approximately 3.732.
  • Step 6: Plug in the values. Height = 25 meters * 3.732.
  • Step 7: Perform the multiplication. Height = 25 * 3.732 = 93.3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the wall and the distance from the wall.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the wall is the opposite side, the distance from the wall is the adjacent side, and the angle of elevation is given.
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