A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

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30 degrees
36.87 degrees
45 degrees
60 degrees

Questions & Step-by-step Solutions

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Q: A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

Solution: Using tan(θ) = height/distance, we have tan(θ) = 30/40 = 0.75. Therefore, θ = tan⁻¹(0.75) ≈ 36.87 degrees.

Steps: 9

Step 1: Identify the height of the building, which is 30 meters.
Step 2: Identify the distance from the point to the base of the building, which is 40 meters.
Step 3: Understand that we need to find the angle of elevation (θ) to the top of the building.
Step 4: Use the tangent function, which relates the angle to the opposite side (height) and the adjacent side (distance).
Step 5: Set up the equation: tan(θ) = height/distance, which is tan(θ) = 30/40.
Step 6: Simplify the fraction: 30/40 = 0.75.
Step 7: Now we have tan(θ) = 0.75.
Step 8: To find θ, use the inverse tangent function: θ = tan⁻¹(0.75).
Step 9: Calculate θ using a calculator: θ ≈ 36.87 degrees.

A building is 30 meters tall. From a point 40 meters away from the base of the building, what is the angle of elevation to the top of the building?

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