Question

solve for x to the nearest tenth.

Explanation:

Step1: Find hypotenuse of lower right - triangle

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$. Here $a = 7$ and $b = 10$, so $c=\sqrt{7^{2}+10^{2}}=\sqrt{49 + 100}=\sqrt{149}$.

Step2: Find $x$ using Pythagorean theorem

In the upper right - triangle, one side is 4 and the hypotenuse is $\sqrt{149}$. Let the other side be $x$. Then $x=\sqrt{(\sqrt{149})^{2}-4^{2}}=\sqrt{149 - 16}=\sqrt{133}$.

Step3: Approximate the value of $x$

$\sqrt{133}\approx11.5$.

Answer:

$11.5$