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

5.5 inches

Step-by-step 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(1ft)/(12in)=5ft+(5)/(12)ft=(65)/(12)ft`

Half this length is,

`((65)/(12))/(2)ft=(65)/(12\cdot2)ft=(65)/(24)ft`

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

`6ft+4in=6ft+4in\cdot(1ft)/(12in)=6ft+(1)/(3)ft=(19)/(3)ft`

Half his height is,

`((19)/(3)ft)/(2)=(19)/(3\cdot2)ft=(19)/(6)ft`

The difference is,

`(19)/(6)ft-(65)/(24)ft=(11)/(24)ft`

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

`(11)/(24)ft\cdot(12in)/(1ft)=(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.