Question

When the angle of elevation of the sun is 62°, a telephone

pole that is tilted at an angle of 8° directly away from the sun
casts a shadow 20 feet long. Determine the length of the pole
to the nearest tenth of a foot.

Answer 1

30.0 ft

Explanation:

You want the length of a pole whose shadow is 20 ft long when the angle of elevation of the sun is 62° and the pole is tilted 8° away from the sun.

Law of Sines

Referring to the attached diagram, we see that the interior angle at B of triangle ABC is 90° -8° = 82°. This makes the interior angle at A ...

A = 180° -82° -62° = 36°

The law of sines tells us side lengths are proportional to the sines of the opposite angles:

c/sin(C) = a/sin(A)

c = a×sin(C)/sin(A) = 20×sin(62°)/sin(36°) ≈ 30.043 . . . feet

The length of the pole is about 30.0 feet.