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A man is 50 meters away from a building. If he looks up at an angle of 60 degree

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Question: A man is 50 meters away from a building. If he looks up at an angle of 60 degrees to see the top of the building, what is the height of the building?

Options:

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

Correct Answer: 40 meters

Solution: 

Height = distance * tan(angle) = 50 * √3 = 50 * 1.732 = 86.6 meters.

A man is 50 meters away from a building. If he looks up at an angle of 60 degree

Practice Questions

Q1
A man is 50 meters away from a building. If he looks up at an angle of 60 degrees to see the top of the building, what is the height of the building?
  1. 25 meters
  2. 30 meters
  3. 35 meters
  4. 40 meters

Questions & Step-by-Step Solutions

A man is 50 meters away from a building. If he looks up at an angle of 60 degrees to see the top of the building, what is the height of the building?
Correct Answer: 86.6 meters
  • Step 1: Understand the situation. A man is standing 50 meters away from a building and looking up at an angle of 60 degrees to see the top of the building.
  • Step 2: Visualize the scenario. Imagine a right triangle where one side is the height of the building, the other side is the distance from the man to the building (50 meters), and the angle between the ground and the line of sight to the top of the building is 60 degrees.
  • 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 man to the building).
  • Step 4: Write the formula. The formula is: Height = distance * tan(angle). Here, distance is 50 meters and angle is 60 degrees.
  • Step 5: Find the value of tan(60 degrees). The value of tan(60 degrees) is √3, which is approximately 1.732.
  • Step 6: Substitute the values into the formula. Height = 50 * tan(60 degrees) = 50 * √3.
  • Step 7: Calculate the height. Height = 50 * 1.732 = 86.6 meters.
  • Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
  • Right Triangle Properties – The question involves the properties of right triangles, where the height of the building represents the opposite side and the distance from the building represents the adjacent side.
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