A building is 30 meters tall. From a point 40 meters away from the base of the b

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?

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?

Correct Answer: 36.87 degrees

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.

Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to calculate the angle of elevation using the ratio of opposite to adjacent sides.
Angle of Elevation – The question involves determining the angle formed by a horizontal line from the observer's point to the top of the building.