Question

A photographer has climbed a building to take a winning shot of a park. If the park is 30 m away and the angle of depression from his sightline is 40°, how high up is the photographer?

a) 20 m
b) 25 m
c) 30 m
d) 40 m

Answer 1

The photographer is approximately 25.173 m above the ground, calculated using the tangent of the 40° angle of depression and 30 m horizontal distance. The closest answer choice is 25 m.

Step-by-step explanation:

The subject in question involves using trigonometric principles to calculate the height of the photographer above the ground. Given the angle of depression is 40° and the horizontal distance to the park is 30 m, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. To find the height of the photographer (opposite side), we calculate:

tan(angle of depression) = opposite side / adjacent side

tan(40°) = height / 30 m
Height = 30 m × tan(40°)
Using a calculator, tan(40°) ≈ 0.8391.
Height ≈ 30 m × 0.8391
Height ≈ 25.173 m
The closest answer choice to this calculation is b) 25 m.