Question

Dr. Black is standing 13 feet from a streetlamp. The lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50. To the nearest foot, the streetlamp is about _____.

Answer 1

26 ft height

Explanation:

The distance between the streetlamp and the tip of his shadow is 9 + 13 = 22 ft.

A rectangle triangle is formed in which one side is 22 ft long and the other side is the streetlamp height. The angle between the 22 ft side and the hypotenuse is 50°. From tangent definition:

tan(50°) = (streetlamp height)/(22 ft)

tan(50°) * (22 ft) = streetlamp height

26 ft = streetlamp height

Answer 2

Distance from tip of shadow to lamp post = 13 +9 feet = 22 ft Height of lamp post = x tan 50 = x /22 = 1.192 x = 22 * 1.192 =.26.2 ft. rounded = 26ft