Question

two cars leave the same parking lot, with one heading north and the other heading east. after several minutes, the eastbound car has traveled 8.2 kilometers. if the two cars are now a straight - line distance of 9.6 kilometers apart, how far has the northbound car traveled? if necessary, round to the nearest tenth.
____ kilometers

Explanation:

Step1: Define Pythagorean variables

Let $a=8.2$ km (eastbound), $c=9.6$ km (straight line), $b$ = northbound distance.

Step2: Rearrange Pythagorean theorem

$b = \sqrt{c^2 - a^2}$

Step3: Substitute values into formula

$b = \sqrt{9.6^2 - 8.2^2}$

Step4: Calculate squared terms

$9.6^2 = 92.16$, $8.2^2 = 67.24$

Step5: Compute difference inside root

$92.16 - 67.24 = 24.92$

Step6: Take square root and round

$\sqrt{24.92} \approx 5.0$

Answer:

5.0 kilometers