Can anyone please solve this problem?

Question

Josh observes a traffic sign across a road some distance from where he stands. He wants to know the height of the sign. His angle of elevation to the top of the sign is 11°. Anna is standing 15 m away from Josh and 28 m away from the sign. She tells Josh that from her position, the angle between Josh and the sign is 53°. What is the height, h, of the sign to the nearest tenth of a metre?

Answer 1

The given information requires the Law of Cosines to find first the distance d from Josh to the sign.

d² = 28² + 15² - 2 (28) (15) cos 53^° = 503.5, d = 22.44 m (don't round more than this for intermediate results).

Then for an elevation angle of 11^° from Josh to the top of the sign, tan 11^° = h / d and h = (22.44) (0.1944) = 4.4 m.