Question

two cars leave the same parking lot, with one heading north and the other heading east. after several minutes, the northbound car has traveled 6.8 kilometers, and the eastbound car has traveled 3.3 kilometers. measured in a straight line, how far apart are the two cars? if necessary, round to the nearest tenth. kilometers

Explanation:

Step1: Identify the right - angled triangle

The paths of the two cars form a right - angled triangle, with the distances traveled by the cars as the two legs of the triangle. Let $a = 6.8$ km and $b=3.3$ km, and the straight - line distance between the cars be $c$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 6.8$ and $b = 3.3$ into the formula: $c=\sqrt{(6.8)^{2}+(3.3)^{2}}=\sqrt{46.24 + 10.89}=\sqrt{57.13}$.

Step3: Calculate the value of $c$

$\sqrt{57.13}\approx7.6$ (rounded to the nearest tenth).

Answer:

$7.6$