Question

The height of a street light is 23 feet. It casts a 12-foot shadow. At the same time, a man

standing next to the street light casts a 3-foot shadow. How tall is the man? If needed,
round the answer to the nearest hundredth.
The man is
feet tall.

Answer 1

Explanation:

this creates 2 similar triangles.

that means all angles are the same. and all the side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.

3 × f = 12

f = 12/3 = 4

now, the same factor applies also to the relation of the heights :

x = height of the man

x × 4 = 23

x = 23/4 = 5.75 ft

the man is 5.75 ft (= 5' 9") tall.