Question

The length of the hypotenuse of a 45°-45°-90° triangleis 10. What is the length of one leg?✓Submit

Answer 1

Since the triangle has two congruent angles (45° and 45°), it is an isosceles triangle, and the legs in this case have the same length (x).

Using the Pythagorean theorem, we have:

$\begin{gathered} 10^2=x^2+x^2 \\ 100=2x^2 \\ x^2=50 \\ x=\sqrt[]{50}=5\sqrt[]{2} \end{gathered}$

So one leg has a length of 5√2.