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A person is standing 40 meters away from a tower. If the angle of elevation to t

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Question: A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?

Options:

  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 45 meters

Correct Answer: 40 meters

Solution: 

Height = distance * tan(angle) = 40 * 1 = 40 meters.

A person is standing 40 meters away from a tower. If the angle of elevation to t

Practice Questions

Q1
A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?
  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 45 meters

Questions & Step-by-Step Solutions

A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?
Correct Answer: 40 meters
  • Step 1: Understand the problem. You have a person standing 40 meters away from a tower and looking up at the top of the tower.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the tower is 45 degrees.
  • Step 3: Recall the relationship between the angle of elevation, the height of the tower, and the distance from the tower. This can be calculated using the tangent function.
  • Step 4: Use the formula for height: Height = distance * tan(angle). Here, the distance is 40 meters and the angle is 45 degrees.
  • Step 5: Calculate tan(45 degrees). The tangent of 45 degrees is 1.
  • Step 6: Substitute the values into the formula: Height = 40 meters * 1.
  • Step 7: Calculate the height. The height of the tower is 40 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the tower and the angle of elevation.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
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