Final answer:
The angle of elevation of the church tower from the man's perspective is approximately 7.13 degrees, determined by using tangent which is the opposite side divided by the adjacent side in a right-angled triangle.
Step-by-step explanation:
The question asks to find the angle of elevation of the top of a church tower from the man's position. To do this, we can use trigonometry, specifically the tangent function, which relates the opposite side (height of the tower) to the adjacent side (distance from the man to the tower) of a right-angled triangle. The formula to find the angle of elevation, θ, is given by:
tan(θ) = opposite/adjacent
Here, the opposite side is the height of the church tower (15 meters) and the adjacent side is the distance from the man (120 meters). So:
tan(θ) = 15 / 120 = 0.125
To find the angle of elevation, we take the arctangent (inverse of tangent) of 0.125. Using a calculator, we get:
θ = arctan(0.125) ≈ 7.13°
Therefore, the angle of elevation is approximately 7.13 degrees.