Question

After a windstorm, a leaning pole makes a 75° angle with the road surface. The pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. About how long is the pole?

a) 11.0 ft.
b) 12.2 ft.
c) 16.7 ft.
d) 20.5 ft.

Answer 1

9514 1404 393

Answer:

b) 12.2 ft

Explanation:

Based on the attached and the answer choices, it looks like we're to assume the pole is leaning away from the sun. Of course, we must assume the angle the pole makes with the ground and the angle of elevation are in the same plane.

The problem can be solved using the law of sines. In the attached, we have ...

AD/sin(O) = OA/sin(D)

The angle at D is 180° -45° -75° = 60°, so this can be written as ...

AD = sin(45°)(15 ft)/sin(60°)

AD ≈ 12.247 ft

The pole is about 12.2 feet long.