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, $c = 16$, $a = 11$, and $b=x$. So, $x^{2}+11^{2}=16^{2}$.

Step2: Rearrange the equation

$x^{2}=16^{2}-11^{2}$.

Step3: Calculate the squares

$16^{2}=256$ and $11^{2}=121$. Then $x^{2}=256 - 121=135$.

Step4: Solve for $x$

$x=\sqrt{135}\approx11.62$.

Answer:

$11.62$