Question

one of the legs of a right triangle measures 9 cm and the other leg measures 1 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c^{2}=a^{2}+b^{2}$.
Let $a = 9$ cm and $b = 1$ cm. Then $c^{2}=9^{2}+1^{2}$.

Step2: Calculate $a^{2}+b^{2}$

$9^{2}+1^{2}=81 + 1=82$. So $c^{2}=82$.

Step3: Solve for $c$

$c=\sqrt{82}$. Using a calculator, $c\approx9.1$ cm.

Answer:

$9.1$ cm