Question

question one of the legs of a right triangle measures 5 cm and its hypotenuse measures 13 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the known leg be $a = 5$ cm and the hypotenuse be $c=13$ cm. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $b$ is the unknown leg. We can rewrite it to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 5$ and $c = 13$ into the formula: $b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}$.

Step3: Calculate the square - root

$\sqrt{144}=12$ cm.

Answer:

$12$ cm