Question

How much longer must the minimum length of a plane mirror be for a 6 ft 4 in man to see his complete head-to-toe image than for a 5 ft 5 in woman to do so? answer in:_____in

Answer 1

ANSWER

5.5 inches

EXPLANATION

For a person to see their full image on a plane mirror, the mirror must be half as long as the person's height. This is because the incidence angle is equal to the reflection angle.

So, for a 5 ft 5 in woman to see her full image in a plane mirror, the mirror must be half her height. Let's convert her height to feet first, knowing that 1 foot is equal to 12 inches,

$5ft+5in=5ft+5in\cdot\frac{1ft}{12in}=5ft+\frac{5}{12}ft=\frac{65}{12}ft$

Half this length is,

$\frac{\frac{65}{12}}{2}ft=\frac{65}{12\cdot2}ft=\frac{65}{24}ft$

The height of the 6 ft 4 in man in feet is,

$6ft+4in=6ft+4in\cdot\frac{1ft}{12in}=6ft+\frac{1}{3}ft=\frac{19}{3}ft$

Half his height is,

$\frac{\frac{19}{3}ft}{2}=\frac{19}{3\cdot2}ft=\frac{19}{6}ft$

The difference is,

$\frac{19}{6}ft-\frac{65}{24}ft=\frac{11}{24}ft$

This is less than 1 foot, so let's convert this back to inches,

$\frac{11}{24}ft\cdot\frac{12in}{1ft}=\frac{11}{2}in=5.5in$

Hence, the minimum length of a plane mirror for a 6'4'' man to see his complete image must be 5.5 inches longer than for a 5'5'' woman to see her full image in the same mirror.