A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
Practice Questions
1 question
Q1
A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
100 m
50 m
75 m
25 m
Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.
Questions & Step-by-step Solutions
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Q
Q: A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
Solution: Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.
Steps: 8
Step 1: Understand the problem. A man is standing 100 meters away from a building.
Step 2: Identify the angle of elevation to the top of the building, which is 45 degrees.
Step 3: Recall the tangent function in trigonometry: tan(angle) = opposite side / adjacent side.
Step 4: In this scenario, the 'opposite side' is the height of the building, and the 'adjacent side' is the distance from the man to the building (100 meters).
Step 5: Write the equation using the tangent function: tan(45°) = height / 100.
Step 6: Know that tan(45°) equals 1. So, the equation becomes: 1 = height / 100.
Step 7: To find the height, multiply both sides of the equation by 100: height = 100 * 1.
Step 8: Calculate the height: height = 100 meters.
