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A tower is 60 m high. From a point on the ground, the angle of elevation to the

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Question: A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)

Options:

  1. 30 m
  2. 40 m
  3. 50 m
  4. 60 m

Correct Answer: 30 m

Exam Year: 2023

Solution: 

Distance = height / tan(angle) = 60 / tan(60) = 60 / √3 ≈ 30 m.

A tower is 60 m high. From a point on the ground, the angle of elevation to the

Practice Questions

Q1
A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
  1. 30 m
  2. 40 m
  3. 50 m
  4. 60 m

Questions & Step-by-Step Solutions

A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
  • Step 1: Understand the problem. We have a tower that is 60 meters high and we want to find out how far a point on the ground is from the base of the tower.
  • Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the base).
  • Step 4: Set up the equation. We can write the equation as: tan(60 degrees) = height / distance.
  • Step 5: Plug in the values. We know the height is 60 meters, so we have: tan(60) = 60 / distance.
  • Step 6: Rearrange the equation to find distance. This gives us: distance = height / tan(60).
  • Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 8: Substitute tan(60) into the equation. Now we have: distance = 60 / √3.
  • Step 9: Simplify the calculation. This can be approximated as distance ≈ 30 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tower and the angle of elevation to find the horizontal distance.
  • 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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