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A person is looking at the top of a 40-meter tall building from a distance of 50
A person is looking at the top of a 40-meter tall building from a distance of 50 meters. What is the angle of elevation?
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Practice Questions
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Q1
A person is looking at the top of a 40-meter tall building from a distance of 50 meters. What is the angle of elevation?
30 degrees
36.87 degrees
45 degrees
53.13 degrees
Show Solution
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tan(θ) = height/distance = 40/50, θ = tan⁻¹(0.8) ≈ 38.66 degrees.
Questions & Step-by-step Solutions
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Q
Q: A person is looking at the top of a 40-meter tall building from a distance of 50 meters. What is the angle of elevation?
Solution:
tan(θ) = height/distance = 40/50, θ = tan⁻¹(0.8) ≈ 38.66 degrees.
Steps: 7
Show Steps
Step 1: Identify the height of the building, which is 40 meters.
Step 2: Identify the distance from the person to the base of the building, which is 50 meters.
Step 3: Use the formula for the tangent of the angle of elevation: tan(θ) = height/distance.
Step 4: Substitute the values into the formula: tan(θ) = 40/50.
Step 5: Simplify the fraction: 40/50 = 0.8.
Step 6: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(0.8).
Step 7: Calculate θ using a calculator: θ ≈ 38.66 degrees.
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