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

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Question: A man is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 30 degrees, what is the height of the tower?

Options:

  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 10√3 meters

Correct Answer: 20√3 meters

Solution: 

Height = distance * tan(30) = 40 * (1/√3) = 40/√3 = 20√3 meters.

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

Practice Questions

Q1
A man is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 30 degrees, what is the height of the tower?
  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 10√3 meters

Questions & Step-by-Step Solutions

A man is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 30 degrees, what is the height of the tower?
  • Step 1: Understand the problem. We have a man standing 40 meters away from a tower and we need to find the height of the tower using the angle of elevation, which is 30 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where the man is at one point, the top of the tower is the second point, and the base of the tower is the third point.
  • Step 3: Identify the sides of the triangle. The distance from the man to the tower is the base (40 meters), the height of the tower is the opposite side, and the angle of elevation (30 degrees) is between the base and the line of sight to the top of the tower.
  • Step 4: Use the tangent function. 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 man to the tower). So, tan(30 degrees) = height / 40.
  • Step 5: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 6: Set up the equation. We can write the equation as height / 40 = 1/√3.
  • Step 7: Solve for height. Multiply both sides by 40 to get height = 40 * (1/√3).
  • Step 8: Simplify the height. This gives us height = 40/√3. We can also express this as height = 20√3 meters by rationalizing the denominator.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tower and the distance from the tower.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the tower, the ground, and the line of sight.
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