Question

in a a 45-45-90 triangle with a hypotenuse of 6[SQRT(6)], what is the length of one leg?

Answer 1

you need to use the sin of 45 to get your answer. sin=O/H (SOHCAHTOA) so sin45=x/6√6. Multiply both sides by 6√6 and you will get (6√6)sin45=x. X being your leg measure. if you type that into your calculator you will get approx 12.506.

Answer 2

In case you don't even know what sin is:

For every 45-45-90 triangle, hypotenuse is \(\sqrt2\) times larger than side leg.

Since you are given that hypotenuse is \(6\sqrt6 = 6\sqrt2\sqrt3\)

You can divide it by \(\sqrt{2}\) to get side leg. \[\dfrac{6\sqrt6}{\sqrt{2}} = \dfrac{6\sqrt2\sqrt3}{\sqrt{2}} = \boxed{6\sqrt3}\]