# How do you solve the right triangle given the Hypotenuse side is 7 and it is a 45-45-90 triangle?

Nov 4, 2015

The two catheti are equal and they measure $\frac{7}{\sqrt{2}}$

#### Explanation:

If the two acute angles are equal, it means that the two catheti are also equal. If ${c}_{1}$ and ${c}_{2}$ are the two catheti and $h$ is the hypothenuse, then Pitagora's theorem states that

${h}^{2} = {c}_{1}^{2} + {c}_{2}^{2}$.

But in our case, ${c}_{1} = {c}_{2}$, so we have

${h}^{2} = 2 {c}_{1}^{2}$, and thus

${c}_{1} = \frac{h}{\sqrt{2}}$, since we can't accept negative solutions.