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, $c = 14$ and one leg $a = 12$, and we want to find the other leg $x$. So, $x^{2}+12^{2}=14^{2}$.

Step2: Rearrange the equation

$x^{2}=14^{2}-12^{2}$.

Step3: Calculate the squares

$14^{2}=196$ and $12^{2}=144$. Then $x^{2}=196 - 144=52$.

Step4: Solve for $x$

$x=\sqrt{52}\approx7.21$

Answer:

$7.21$