Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth. 14 10 x

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $c = 14$, $b = 10$, and we want to find $a=x$. So, $x^{2}+10^{2}=14^{2}$.

Step2: Rearrange the equation

$x^{2}=14^{2}-10^{2}$.

Step3: Calculate the squares

$14^{2}=196$ and $10^{2}=100$. Then $x^{2}=196 - 100=96$.

Step4: Solve for $x$

$x=\sqrt{96}$.

Step5: Round to the nearest hundredth

$x\approx9.80$.

Answer:

$9.80$