Question

Mr. Math is 6 feet tall and cast a shadow of 5 feet. If a flagpole cast a shadow of 27 feet, how tall is the flagpole?

Answer 1

32.4 feet

Explanation:

Height and length of the shadow would be in the same ratio

6 : 5

X : 27

6/5 = X/27

X = 27 × 6/5

X = 32.4

Answer 2

32.4 ft

Explanation:

See the attachment.

Clearly, Mr. Math and his shadow create a right triangle, as do the flagpole and its shadow. These triangles are similar, which means corresponding sides are in the same ratio.

Mr. Math's height of 6 ft corresponds to the flagpole's height of x ft (we want to find x). Mr. Math's shadow of 5 ft corresponds to the flagpole's shadow of 27 ft. So, set up the proportion:

`(6)/(x) =(5)/(27)`

Cross-multiply:

5x = 6 * 27 = 162

x = 162/5 = 32.4 ft