Question

right triangle relationships and trigonometry
the hypotenuse of a 45 - 45 - 90 triangle measures 7√2 units.
what is the length of one leg of the triangle?

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 right - triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the hypotenuse $c$ is related to the legs $a$ and $b$ (since $a = b$) by $c=a\sqrt{2}$.

Step2: Solve for the leg length

Given $c = 7\sqrt{2}$, and $c=a\sqrt{2}$. Then $a\sqrt{2}=7\sqrt{2}$. Divide both sides by $\sqrt{2}$, we get $a = 7$.

Answer:

7 units