Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a = 16 miles and c = 34 miles, what is b? if necessary, round to the nearest tenth. b = miles

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 $a = 16$ and $c = 34$, we substitute into the formula: $b=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $34+16 = 50$ and $34 - 16=18$. Then $b=\sqrt{50\times18}=\sqrt{900}$.

Step3: Calculate the square root

$\sqrt{900}=30$.

Answer:

$30$