Question

one of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let one leg $a = 3$ cm and hypotenuse $c=16$ cm. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $b$ is the other leg. We can rewrite it as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 3$ and $c = 16$ into the formula: $b=\sqrt{16^{2}-3^{2}}=\sqrt{256 - 9}=\sqrt{247}$.

Step3: Calculate and round

$\sqrt{247}\approx15.7$ (rounded to the nearest tenth).

Answer:

$15.7$ cm