Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a = 7 feet and c = 10 feet, what is b? if necessary, round to the nearest tenth. b = feet

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$. We want to find $b$, so we can rewrite the formula as $b = \sqrt{c^{2}-a^{2}}$.

Step2: Substitute given values

Given $a = 7$ and $c = 10$, we substitute into the formula: $b=\sqrt{10^{2}-7^{2}}=\sqrt{100 - 49}=\sqrt{51}$.

Step3: Calculate and round

$\sqrt{51}\approx7.1$

Answer:

$7.1$