Question

the hypotenuse of a right triangle measures 13 cm and one of its legs measures 12 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c$, one leg be $a$ and the other leg be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We know $c = 13$ and $a = 12$, and we want to find $b$. So, $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $c = 13$ and $a = 12$ into the formula $b^{2}=c^{2}-a^{2}$. We get $b^{2}=13^{2}-12^{2}=169 - 144=25$.

Step3: Solve for $b$

Take the square - root of both sides. Since $b>0$ (as it represents the length of a side of a triangle), $b=\sqrt{25}=5$.

Answer:

5