Question

In a 45°- 45°- 90° right triangle, the length of the hypotenuse is 15. How long are the legs?

Answer 1

`(15sqrt2)/2`

Explanation:

The legs and hypotenuse are in a `1:sqrt2` ratio in this special triangle
so if the hypotenuse is 15 the legs are `15/sqrt2`

you can think of it like this:

`x/15=1/sqrt2`
`x=15/sqrt2`

now to rationalize...
`15/sqrt2 *sqrt2/sqrt2= (15sqrt2)/2`