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, $x$ and 8 are the legs and 15 is the hypotenuse. So, $x^{2}+8^{2}=15^{2}$.

Step2: Rearrange the equation

We get $x^{2}=15^{2}-8^{2}$. Calculate $15^{2}=225$ and $8^{2}=64$. Then $x^{2}=225 - 64=161$.

Step3: Solve for $x$

Take the square root of both sides: $x=\sqrt{161}$. Rounding to the nearest hundredth, $x\approx12.69$.

Answer:

$12.69$