Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $a = 5$, $b = 6$, and $x$ is the hypotenuse. So $x=\sqrt{5^{2}+6^{2}}$.

Step2: Calculate the values

First, calculate $5^{2}=25$ and $6^{2}=36$. Then $5^{2}+6^{2}=25 + 36=61$. So $x=\sqrt{61}$.

Step3: Round the result

$\sqrt{61}\approx7.81$

Answer:

$7.81$