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 5 kilometers. If the two cars are now a straight-line distance of 8 kilometers apart, how far has the northbound car traveled? If necessary, round to the nearest tenth.

Answer 1

The northbound car has traveled a distance of 6.2 miles.

Step-by-step explanation:

Step 1:

The eastbound car has traveled a distance of 5 miles and if a straight line is drawn between the two car's positions it would measure 8 miles.

This forms a triangle which has a hypotenuse measuring 8 miles while one of the other sides measures 5 miles.

Assume the distance traveled by the northbound car is x miles.

Step 2:

According to Pythagoras' theorem,

$x^{2} +5^{2} =8^{2} , x^{2} = 8^{2} -5^{2} = 64-25.$

$x^{2} =39, x=6.2449.$

So the northbound car has traveled a distance of 6.244 miles. Rounding this off, we get 6.2 miles.