find hypotenuse of 45-45-90 triangle
Check the final answer first, then review the worked steps.
Problem
find hypotenuse of 45-45-90 triangle
Step-by-step solution
In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, $\sin(45^{\circ}) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{x}$. Since $\sin(45^{\circ}) = \frac{1}{\sqrt{2}}$, we have $\frac{1}{\sqrt{2}} = \frac{7}{x}$, so $x = 7\sqrt{2}$.
Answer
7\sqrt{2}