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A person is standing 30 meters away from a building. If the angle of elevation t

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Question: A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60°, what is the height of the building?

Options:

  1. 15√3 meters
  2. 30 meters
  3. 15 meters
  4. 20 meters

Correct Answer: 15√3 meters

Solution: 

Height = distance * tan(60°) = 30 * √3 = 15√3 meters.

A person is standing 30 meters away from a building. If the angle of elevation t

Practice Questions

Q1
A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60°, what is the height of the building?
  1. 15√3 meters
  2. 30 meters
  3. 15 meters
  4. 20 meters

Questions & Step-by-Step Solutions

A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60°, what is the height of the building?
  • Step 1: Understand the problem. You have a person standing 30 meters away from a building and looking up at the top of the building at an angle of 60°.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building (which we want to find), the other side is the distance from the person to the building (30 meters), and the angle between the ground and the line of sight to the top of the building is 60°.
  • Step 3: Use 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 person to the building). So, tan(60°) = height / 30.
  • Step 4: Rearrange the formula to find the height. Multiply both sides by 30: height = 30 * tan(60°).
  • Step 5: Calculate tan(60°). The value of tan(60°) is √3.
  • Step 6: Substitute the value of tan(60°) into the equation: height = 30 * √3.
  • Step 7: Simplify the expression. The height of the building is 30√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from it.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the angle of elevation.
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