Question

A 12-foot flag pole casts a shadow that is 15 feet long. Which proportion can be used to determine the length of the mans shadow at the same time of day?

Answer 1

`(5)/(4) ×Height`

Explanation:

Height of the pole = 12 foot

Shadow length =15 foot

Lets assume an angle α which is the angle between the line joining the far end of the shadow of pole and pole.

Then tan(α) = 12/15 =4/5

Now suppose that height of a random man be H and length of shadow is S.

Now by using the same angle α because we are at the same time of the day.

`tan(\alpha )=(H)/(S)`

`(4)/(5)=(H)/(S)`

`S =(5H)/(4)`

Hence the proportion factor is =5/4.