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From a point 25 meters away from the base of a building, the angle of elevation

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Question: From a point 25 meters away from the base of a building, the angle of elevation to the top of the building is 30 degrees. What is the height of the building?

Options:

  1. 25/√3 meters
  2. 15 meters
  3. 20 meters
  4. 10 meters

Correct Answer: 25/√3 meters

Solution: 

Using tan(30) = height / 25, height = 25 * tan(30) = 25 * (1/√3) = 25/√3 meters.

From a point 25 meters away from the base of a building, the angle of elevation

Practice Questions

Q1
From a point 25 meters away from the base of a building, the angle of elevation to the top of the building is 30 degrees. What is the height of the building?
  1. 25/√3 meters
  2. 15 meters
  3. 20 meters
  4. 10 meters

Questions & Step-by-Step Solutions

From a point 25 meters away from the base of a building, the angle of elevation to the top of the building is 30 degrees. What is the height of the building?
  • Step 1: Understand the problem. You are looking for the height of a building from a point 25 meters away.
  • Step 2: Identify the angle of elevation. The angle given is 30 degrees.
  • Step 3: Recall the tangent function in a right triangle. The tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the building).
  • Step 4: Set up the equation using the tangent function: tan(30 degrees) = height / 25 meters.
  • Step 5: Solve for height. Rearrange the equation to find height: height = 25 * tan(30 degrees).
  • Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 7: Substitute the value of tan(30 degrees) into the equation: height = 25 * (1/√3).
  • Step 8: Simplify the equation: height = 25/√3 meters.
  • Trigonometry – The problem tests the understanding of right triangle relationships, specifically using the tangent function to find the height of a building based on an angle of elevation.
  • Angle of Elevation – The question involves interpreting the angle of elevation from a horizontal distance to determine vertical height.
  • Right Triangle Properties – The problem requires knowledge of how to relate the sides of a right triangle using trigonometric ratios.
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