Question

the hypotenuse of a right triangle measures 18 cm and one of its legs measures 10 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

Let the hypotenuse be $c$, and the legs be $a$ and $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We know $c = 18$ and $a = 10$, and we want to find $b$. So, $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $c = 18$ and $a = 10$ into the formula $b^{2}=c^{2}-a^{2}$. We get $b^{2}=18^{2}-10^{2}=324 - 100=224$.

Step3: Solve for $b$

Take the square - root of both sides: $b=\sqrt{224}\approx14.9666\approx15.0$.

Answer:

$15.0$ cm