A person is standing 40 m away from a building and observes the top of the build
Practice Questions
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)
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Questions & Step-by-Step Solutions
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)
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.
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.
Angle of Elevation – Understanding how to apply the angle of elevation in a right triangle to find the height of an object.
Units and Rounding – The importance of correctly interpreting and rounding the final answer in the context of the problem.
