Question

the hypotenuse of a right triangle measures 7 cm and one of its legs measures 2 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 7$ cm and one leg be $a = 2$ 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 $c = 7$ and $a = 2$ into the formula: $b=\sqrt{7^{2}-2^{2}}=\sqrt{49 - 4}=\sqrt{45}$.

Step3: Calculate and round

$\sqrt{45}\approx6.7$ (rounded to the nearest tenth).

Answer:

$6.7$ cm