Question

a 45 - 45 - 90 triangle has a hypotenuse with a length of 10 feet. what are the lengths of the other legs? 7.07 ft. 9.14 ft. 8.46 ft. 6.36 ft.

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the hypotenuse is $\sqrt{2}$ times the length of each leg. Let the length of each leg be $x$. Then the hypotenuse $c = x\sqrt{2}$.

Step2: Solve for $x$

We know $c = 10$ feet and $c=x\sqrt{2}$. So, $x=\frac{c}{\sqrt{2}}$. Substituting $c = 10$ into the formula, we get $x=\frac{10}{\sqrt{2}}=\frac{10\sqrt{2}}{2}=5\sqrt{2}\approx5\times1.414 = 7.07$ feet.

Answer:

7.07 ft.