Question

rachel is playing hide - and - seek with norma and jamie. norma is hiding 8.6 meters south of rachel, and jamie is hiding due east of norma. if rachel is 9.6 meters from jamie, how far apart are norma and jamie? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the right - triangle

Rachel, Norma, and Jamie form a right - triangle. The distance between Rachel and Norma ($a = 8.6$ meters) is one leg, the distance between Norma and Jamie is the other leg (let's call it $b$), and the distance between Rachel and Jamie ($c = 9.6$ meters) is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We want to find $b$, so we can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 8.6$ and $c = 9.6$ into the formula:
$b=\sqrt{9.6^{2}-8.6^{2}}=\sqrt{(9.6 + 8.6)(9.6 - 8.6)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).
First, calculate $(9.6 + 8.6)(9.6 - 8.6)=(18.2)\times(1)=18.2$.
Then, $b=\sqrt{18.2}\approx4.3$.

Answer:

$4.3$