Question

A person standing 28 feet from a street light casts a shadow as shown. What is the height h of the street light? Assume the triangles are similar.

Answer 1

Answer:

20 ft

Step-by-step explanation:

Since we assume the triangles are similar, therefore, the ratio of their corresponding sides will be the same.

Height of the bigger triangle corresponds to height of the person

Distance of the person from street light + shadow of the person corresponds to the length of the shadow of the person

Therefore, the ratio of the corresponding sides of the triangles would be:

Height of bigger triangle : height of the person = Distance of the person from street light + shadow of the person : length of the shadow of the person

Thus:

h : 6 = 28 + 12 : 12

h : 6 = 40 : 12

h/6 = 40/12

Cross multiply

12h = 40*6

12h = 240

Divide both sides by 12

12h/12 = 240/12

h = 20

Height of the street light = 20 ft