Question

the hypotenuse of a right triangle measures 17 cm and one of its legs measures 13 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 17$ cm and one leg be $a = 13$ cm. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $b$ is the unknown leg. We can rewrite it as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 17$ and $a = 13$ into the formula: $b=\sqrt{17^{2}-13^{2}}=\sqrt{(17 + 13)(17 - 13)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{30\times4}=\sqrt{120}$.

Step3: Calculate and round

$\sqrt{120}\approx10.95445$. Rounding to the nearest tenth, $b\approx11.0$ cm.

Answer:

$11.0$ cm