Question

find the value of x. round the answer to the nearest tenth if necessary. 11 8 x (not drawn to scale) a 3 b 19 c 7.5 d 13.6

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, $c = 11$, one leg $b = 8$, and the other leg is $x$. So, $x^{2}+8^{2}=11^{2}$.

Step2: Rearrange the equation to solve for $x$

$x^{2}=11^{2}-8^{2}$. Calculate $11^{2}=121$ and $8^{2}=64$. Then $x^{2}=121 - 64=57$.

Step3: Find the value of $x$

$x=\sqrt{57}\approx7.5$.

Answer:

C. 7.5