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From the top of a 40-meter high tower, the angle of depression to a point on the

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Question: From the top of a 40-meter high tower, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the tower?

Options:

  1. 40 meters
  2. 30 meters
  3. 50 meters
  4. 20 meters

Correct Answer: 40 meters

Solution: 

distance = height / tan(45) = 40 / 1 = 40 meters

From the top of a 40-meter high tower, the angle of depression to a point on the

Practice Questions

Q1
From the top of a 40-meter high tower, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the tower?
  1. 40 meters
  2. 30 meters
  3. 50 meters
  4. 20 meters

Questions & Step-by-Step Solutions

From the top of a 40-meter high tower, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the tower?
Correct Answer: 40 meters
  • Step 1: Understand that the tower is 40 meters high.
  • Step 2: Recognize that the angle of depression is the angle formed from the top of the tower down to the point on the ground.
  • Step 3: Note that an angle of depression of 45 degrees means that the angle from the horizontal line down to the point is 45 degrees.
  • Step 4: Use the tangent function, which relates the height of the tower to the distance from the base of the tower. The formula is: tan(angle) = opposite/adjacent.
  • Step 5: In this case, the opposite side is the height of the tower (40 meters) and the adjacent side is the distance we want to find.
  • Step 6: Since the angle is 45 degrees, we know that tan(45 degrees) = 1.
  • Step 7: Set up the equation: tan(45) = height / distance, which simplifies to 1 = 40 / distance.
  • Step 8: Rearrange the equation to find the distance: distance = height / tan(45).
  • Step 9: Substitute the height into the equation: distance = 40 / 1.
  • Step 10: Calculate the distance: distance = 40 meters.
  • Angle of Depression – The angle formed by a horizontal line and the line of sight to an object below the horizontal line.
  • Tangent Function – In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
  • Right Triangle Properties – Understanding the relationships between the sides and angles in a right triangle.
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