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A man is standing 15 meters away from a wall. If he looks up at an angle of 30 d

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Question: A man is standing 15 meters away from a wall. If he looks up at an angle of 30 degrees to see the top of the wall, what is the height of the wall?

Options:

  1. 5 meters
  2. 10 meters
  3. 15 meters
  4. 20 meters

Correct Answer: 10 meters

Solution: 

Height = distance * tan(angle) = 15 * (1/√3) ≈ 15 * 0.577 = 8.66 meters.

A man is standing 15 meters away from a wall. If he looks up at an angle of 30 d

Practice Questions

Q1
A man is standing 15 meters away from a wall. If he looks up at an angle of 30 degrees to see the top of the wall, what is the height of the wall?
  1. 5 meters
  2. 10 meters
  3. 15 meters
  4. 20 meters

Questions & Step-by-Step Solutions

A man is standing 15 meters away from a wall. If he looks up at an angle of 30 degrees to see the top of the wall, what is the height of the wall?
Correct Answer: 8.66 meters
  • Step 1: Understand the situation. A man is standing 15 meters away from a wall.
  • Step 2: He looks up at an angle of 30 degrees to see the top of the wall.
  • Step 3: We need to find the height of the wall using the distance and the angle.
  • Step 4: Use the tangent function from trigonometry. The formula is: Height = distance * tan(angle).
  • Step 5: Plug in the values: Height = 15 meters * tan(30 degrees).
  • Step 6: Know that tan(30 degrees) is equal to 1/√3 or approximately 0.577.
  • Step 7: Calculate the height: Height = 15 * (1/√3) = 15 * 0.577.
  • Step 8: Perform the multiplication: 15 * 0.577 ≈ 8.66 meters.
  • Step 9: Conclude that the height of the wall is approximately 8.66 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 man to the wall is the adjacent side, and the angle of elevation is given.
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