Question

8.9 mi. 8.5 mi. what is the length of the missing leg? if necessary, round to the nearest tenth. b = miles

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse $c = 8.9$ mi and one - leg $a = 8.5$ mi. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{8.9^{2}-8.5^{2}}=\sqrt{(8.9 + 8.5)(8.9 - 8.5)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $8.9+8.5 = 17.4$ and $8.9 - 8.5=0.4$. Then $b=\sqrt{17.4\times0.4}=\sqrt{6.96}$.

Step3: Calculate the square - root and round

$b=\sqrt{6.96}\approx2.6$ mi.

Answer:

$2.6$