Question

A 5.9-foot-tall-man stands near a 12-foot statue. The man places a mirror on the ground a certain distance from the base of the statue, and then stands another 7 feet from the mirror to see the top of the statue in it. How far is the mirror from the base of the statue?

Answer 1

14.24 foot far is the mirror from the base of the statue.

Explanation:

Proportion states that the two ratios or fractions are equal.

As per the statement:

See the diagram as shown below:

Height of a boy = 5.9 foot tall

Height of a statue = 12 foot.

Distance of a boy from the mirror = 7 feet.

Let x be the distance of the mirror from the base of the statue.

then by definition of proportion we have;

`\frac{\text{Height of a boy}}{\text{Distance of a boy from the mirror}}= \frac{\text{Height of a statues}}{\text{Distance of mirror from the base of the statue} }`

Substitute the given values we have;

`(5.9)/(7) =(12)/(x)`

By cross multiply we have;

`5.9x = 84`

Divide both sides by 5.9 we have;

x = 14.24 ft

Therefore, 14.24 foot far is the mirror from the base of the statue.