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

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Question: From the top of a 50-meter high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?

Options:

  1. 50 meters
  2. 100 meters
  3. 25 meters
  4. 70 meters

Correct Answer: 50 meters

Solution: 

Distance = height / tan(angle) = 50 / tan(45°) = 50 meters.

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

Practice Questions

Q1
From the top of a 50-meter high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?
  1. 50 meters
  2. 100 meters
  3. 25 meters
  4. 70 meters

Questions & Step-by-Step Solutions

From the top of a 50-meter high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?
  • Step 1: Understand the problem. We have a building that is 50 meters tall.
  • Step 2: Identify the angle of depression. It is given as 45 degrees.
  • Step 3: Visualize the situation. Draw a right triangle where the height of the building is one side (50 meters) and the distance from the base of the building to the point on the ground is the other side.
  • Step 4: Recall the relationship in a right triangle. The angle of depression from the top of the building to the point on the ground is equal to the angle of elevation from the point on the ground to the top of the building.
  • Step 5: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the base).
  • Step 6: Set up the equation. We have tan(45 degrees) = height / distance.
  • Step 7: Substitute the known values into the equation. We know the height is 50 meters and tan(45 degrees) is 1.
  • Step 8: Solve for distance. Rearranging gives us distance = height / tan(45 degrees) = 50 / 1 = 50 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 right triangles is crucial for solving problems involving heights and distances.
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