A person 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 person 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 person 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 person is standing 100 meters away from a building and looking up at the top of the building.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the building is 45 degrees.
Step 3: Recall the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the building) to the adjacent side (distance from the building).
Step 4: Write the formula for tangent. tan(angle) = height / distance.
Step 5: Substitute the known values into the formula. For 45 degrees, tan(45°) = 1, and the distance is 100 meters.
Step 6: Set up the equation. 1 = height / 100.
Step 7: Solve for height. Multiply both sides by 100 to get height = 100 * 1.
Step 8: Calculate the height. The height of the building is 100 meters.
