Question

the hypotenuse of a right triangle measures 10 cm and one of its legs measures 8 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 10$ cm, one leg be $a = 8$ cm, and the other leg be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $c = 10$ and $a = 8$ into $b^{2}=c^{2}-a^{2}$. We get $b^{2}=10^{2}-8^{2}=100 - 64=36$.

Step3: Solve for $b$

Take the square - root of both sides. Since $b$ represents the length of a side of a triangle, $b=\sqrt{36}=6$ cm.

Answer:

6 cm