A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
Practice Questions
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Q1
A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
20 m
30 m
40 m
50 m
Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.
Questions & Step-by-step Solutions
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Q
Q: A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
Solution: Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.
Steps: 9
Step 1: Understand the problem. A person is standing 40 meters away from a building and sees the top of the building at an angle of 60 degrees.
Step 2: Identify the right triangle formed by the person, the top of the building, and the base of the building.
Step 3: The distance from the person to the building is the base of the triangle, which is 40 meters.
Step 4: The angle of elevation to the top of the building is 60 degrees.
Step 5: Use the tangent function, which relates the angle to the opposite side (height of the building) and the adjacent side (distance from the building).
Step 6: The formula is: Height = distance * tan(angle). Here, Height = 40 m * tan(60 degrees).
Step 7: Calculate tan(60 degrees). It is equal to √3 (approximately 1.732).
Step 8: Multiply: Height = 40 m * √3 ≈ 40 m * 1.732 ≈ 69.28 m.
Step 9: Round the height to the nearest whole number if needed. In this case, it rounds to 69 m.
