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. Here, if $x$ is one of the legs and 8 is the other leg, and 10 is the hypotenuse, then $x^{2}+8^{2}=10^{2}$.

Step2: Rearrange the equation to solve for $x$

$x^{2}=10^{2}-8^{2}$. Calculate $10^{2}=100$ and $8^{2}=64$. So $x^{2}=100 - 64=36$.

Step3: Take the square root of both sides

$x=\sqrt{36}=6$.

Answer:

6