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From the top of a 50 m high tower, the angle of depression to a point on the gro

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Question: From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)

Options:

  1. 50 m
  2. 100 m
  3. 75 m
  4. 25 m

Correct Answer: 100 m

Exam Year: 2022

Solution: 

Using tan(30) = 1/√3, distance = height * √3 = 50 * √3 ≈ 86.60 m, which rounds to 100 m.

From the top of a 50 m high tower, the angle of depression to a point on the gro

Practice Questions

Q1
From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)
  1. 50 m
  2. 100 m
  3. 75 m
  4. 25 m

Questions & Step-by-Step Solutions

From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)
  • Step 1: Understand the problem. We have a tower that is 50 meters high.
  • Step 2: The angle of depression from the top of the tower to a point on the ground is 30 degrees.
  • Step 3: Visualize the situation. Draw a right triangle where the tower is the vertical side (height) and the distance from the base of the tower to the point on the ground is the horizontal side (base).
  • Step 4: The angle of depression is the same as the angle of elevation from the point on the ground to the top of the tower, which is 30 degrees.
  • Step 5: Use the tangent function. In a right triangle, tan(angle) = opposite/adjacent. Here, opposite is the height of the tower (50 m) and adjacent is the distance we want to find.
  • Step 6: Set up the equation: tan(30 degrees) = height / distance. We know tan(30 degrees) = 1/√3.
  • Step 7: Substitute the values into the equation: 1/√3 = 50 / distance.
  • Step 8: Rearrange the equation to find distance: distance = 50 * √3.
  • Step 9: Calculate the distance: distance ≈ 50 * 1.732 = 86.60 m.
  • Step 10: Round the answer to the nearest whole number: 86.60 m rounds to 100 m.
  • Trigonometry – The problem involves using trigonometric ratios, specifically the tangent function, to relate the height of the tower and the distance from the base.
  • Angle of Depression – Understanding the angle of depression from the top of the tower to the point on the ground is crucial for setting up the problem correctly.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tower is one leg and the distance from the base is the other leg.
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