Question

A 6-foot person standing 15 feet from a streetlight casts a 15-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.

Answer 1

I was having trouble found it someone had asked it before

(length of side AC)/(length of side DF) = (length of side BC)/(length of side EF)

(height of man)/(height of flagpole) = (length of man’s shadow)/L

Substituting, we have:
6 ft./150 ft. = 8 ft./L

Cross-multiplying, we get:
(6 ft.)L = (150 ft.)(8 ft.)
(6 ft.)L = 1200 ft.²
L = (1200 ft.²)/6 ft.
L = 200 ft. is the length of the shadow cast by the 150-ft. flagpole.