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From the top of a 50-meter high tower, the angle of depression to a point on the

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Question: From the top of a 50-meter high tower, the angle of depression to a point on the ground is 30°. How far is the point from the base of the tower?

Options:

  1. 25 meters
  2. 30 meters
  3. 35 meters
  4. 40 meters

Correct Answer: 25 meters

Solution: 

Using tan(30°) = height/distance, distance = height/tan(30°) = 50/√3 = 25 meters.

From the top of a 50-meter high tower, the angle of depression to a point on the

Practice Questions

Q1
From the top of a 50-meter high tower, the angle of depression to a point on the ground is 30°. How far is the point from the base of the tower?
  1. 25 meters
  2. 30 meters
  3. 35 meters
  4. 40 meters

Questions & Step-by-Step Solutions

From the top of a 50-meter high tower, the angle of depression to a point on the ground is 30°. How far is the point from the base of the tower?
  • Step 1: Understand that the tower is 50 meters high.
  • Step 2: Recognize that the angle of depression is the angle formed from the top of the tower to the point on the ground.
  • Step 3: Note that the angle of depression is 30 degrees.
  • Step 4: Visualize a right triangle where the height of the tower is one side (50 meters) and the distance from the base of the tower to the point on the ground is the other side.
  • Step 5: Use the tangent function, which relates the angle to the opposite side (height) and the adjacent side (distance).
  • Step 6: Write the formula: tan(30°) = height / distance.
  • Step 7: Substitute the known values into the formula: tan(30°) = 50 / distance.
  • Step 8: Rearrange the formula to find distance: distance = height / tan(30°).
  • Step 9: Calculate tan(30°), which is equal to 1/√3.
  • Step 10: Substitute tan(30°) into the distance formula: distance = 50 / (1/√3).
  • Step 11: Simplify the equation: distance = 50 * √3.
  • Step 12: Calculate the distance: distance = 50 / √3, which is approximately 25 meters.
  • 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 right triangle.
  • Right Triangle Properties – The relationship between the opposite side (height of the tower) and the adjacent side (distance from the base) in a right triangle is key to solving the problem.
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