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A man is 40 meters away from a tower. If he looks at the top of the tower at an

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Question: A man is 40 meters away from a tower. If he looks at the top of the tower at an angle of elevation of 45 degrees, what is the height of the tower?

Options:

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

Correct Answer: 40 meters

Solution: 

Height = distance * tan(45) = 40 * 1 = 40 meters.

A man is 40 meters away from a tower. If he looks at the top of the tower at an

Practice Questions

Q1
A man is 40 meters away from a tower. If he looks at the top of the tower at an angle of elevation of 45 degrees, what is the height of the tower?
  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 50 meters

Questions & Step-by-Step Solutions

A man is 40 meters away from a tower. If he looks at the top of the tower at an angle of elevation of 45 degrees, what is the height of the tower?
  • Step 1: Understand that the man is looking at the top of the tower from a distance of 40 meters.
  • Step 2: Know that the angle of elevation is the angle between the horizontal line (where the man is standing) and the line of sight to the top of the tower.
  • Step 3: The angle of elevation given is 45 degrees.
  • Step 4: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the tower) to the adjacent side (distance from the tower).
  • Step 5: Use the formula: height = distance * tan(angle). Here, distance = 40 meters and angle = 45 degrees.
  • Step 6: Calculate tan(45 degrees), which is equal to 1.
  • Step 7: Substitute the values into the formula: height = 40 * tan(45) = 40 * 1.
  • Step 8: Calculate the height: height = 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 the concept of angle of elevation is crucial for solving problems involving heights and distances.
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