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?

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?

Correct Answer: 38.66 degrees

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.

Trigonometry – The problem involves using the tangent function to find the angle of elevation from a right triangle formed by the height of the building and the distance from the observer.
Angle of Elevation – Understanding the definition of angle of elevation, which is the angle formed by the line of sight above the horizontal.