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From a point 80 meters away from the base of a tower, the angle of elevation to

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Question: From a point 80 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 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(angle) = 80 * (1/√3) = 80 / 1.732 = 46.19 meters.

From a point 80 meters away from the base of a tower, the angle of elevation to

Practice Questions

Q1
From a point 80 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 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

From a point 80 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 degrees. What is the height of the tower?
Correct Answer: 46.19 meters
  • Step 1: Understand the problem. You have a tower and you are standing 80 meters away from its base.
  • Step 2: Identify the angle of elevation. The angle from your line of sight to the top of the tower is 30 degrees.
  • Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the tower) divided by the adjacent side (distance from the tower).
  • Step 4: Write the formula. Height = distance * tan(angle). Here, distance = 80 meters and angle = 30 degrees.
  • Step 5: Find tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
  • Step 6: Substitute the values into the formula. Height = 80 * (1/√3).
  • Step 7: Calculate the height. Height = 80 / 1.732, which is approximately 46.19 meters.
  • 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 height of the tower, the distance from the tower, and the angle of elevation.
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