Question

one of the legs of a right triangle measures 2 cm and its hypotenuse measures 20 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 $a = 2$ cm and the hypotenuse be $c=20$ 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 $a = 2$ and $c = 20$ into the formula: $b=\sqrt{20^{2}-2^{2}}=\sqrt{400 - 4}=\sqrt{396}$.

Step3: Calculate and round

$\sqrt{396}\approx19.9$ cm.

Answer:

$19.9$ cm