Question

what is the length of each leg of the triangle below? 45° 22 90° 45° a. 11 b. $sqrt{22}$ c. 1 d. $sqrt{11}$ e. 15 f. $11sqrt{2}$

Explanation:

Step1: Identify the triangle type

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

Step2: Solve for the leg length

We know that $c = 22$ and $c=a\sqrt{2}$. So, $a=\frac{c}{\sqrt{2}}$. Substitute $c = 22$ into the formula: $a=\frac{22}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{22}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{22\sqrt{2}}{2}=11\sqrt{2}$.

Answer:

F. $11\sqrt{2}$