Question

if the hypotenuse in the following 45° - 45° - 90° triangle has length 15\sqrt{2} cm, how long are the legs? enter the exact answer. the length of each of the two legs is cm. etextbook and media

Explanation:

Step1: Recall the ratio of sides in 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, if the length of each leg is $x$, the length of the hypotenuse is $\sqrt{2}x$.

Step2: Set up an equation

We know the hypotenuse is $15\sqrt{2}$ cm, so $\sqrt{2}x = 15\sqrt{2}$.

Step3: Solve for $x$

Divide both sides of the equation $\sqrt{2}x = 15\sqrt{2}$ by $\sqrt{2}$. We get $x=\frac{15\sqrt{2}}{\sqrt{2}} = 15$.

Answer:

15