Question

find the missing length in the right triangle. if necessary, round to the nearest tenth. 11 mi 17 mi a 168 mi b 14 mi c 13 mi d 84 mi

Explanation:

Step1: Apply Pythagorean theorem

Let the missing side be $x$. The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, if the hypotenuse $c = 17$ mi and one leg $a = 11$ mi, then $x=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$x=\sqrt{17^{2}-11^{2}}=\sqrt{(17 + 11)(17 - 11)}$ (using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$). So $x=\sqrt{(28)(6)}=\sqrt{168}$.

Step3: Calculate and round

$\sqrt{168}\approx12.96\approx13$ mi.

Answer:

C. 13 mi