Question

the hypotenuse of a right triangle measures 8 cm and one of its legs measures 4 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Substitute given values

We know $c = 8$ cm and $a = 4$ cm. Substituting into the formula gives $4^{2}+b^{2}=8^{2}$.

Step3: Simplify the equation

$16 + b^{2}=64$. Then $b^{2}=64 - 16=48$.

Step4: Solve for $b$

$b=\sqrt{48}\approx6.9$ cm (rounded to the nearest tenth).

Answer:

$6.9$ cm