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From a point 40 meters away from the base of a tower, the angle of elevation to

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Question: From a point 40 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√3 meters
  2. 30 meters
  3. 40 meters
  4. 50 meters

Correct Answer: 20√3 meters

Solution: 

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

From a point 40 meters away from the base of a tower, the angle of elevation to

Practice Questions

Q1
From a point 40 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√3 meters
  2. 30 meters
  3. 40 meters
  4. 50 meters

Questions & Step-by-Step Solutions

From a point 40 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: 20√3 meters
  • Step 1: Understand the problem. You have a tower and you are standing 40 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 = 40 meters and angle = 30 degrees.
  • Step 5: Find tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 6: Substitute the values into the formula. Height = 40 * (1/√3).
  • Step 7: Simplify the calculation. Height = 40/√3.
  • Step 8: Further simplify if needed. Height = 40/√3 can be expressed as 20√3 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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