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 15 kilometers. if the two cars are now a straight-line distance of 17 kilometers apart, how far has the northbound car traveled? kilometers

Explanation:

Step1: Identify the right triangle

The paths of the two cars (north and east) and the straight - line distance between them form a right triangle. Let the distance traveled by the north - bound car be \(x\) kilometers, the distance traveled by the east - bound car be \(a = 15\) kilometers, and the straight - line distance (hypotenuse) be \(c=17\) kilometers. By the Pythagorean theorem, \(a^{2}+x^{2}=c^{2}\).

Step2: Substitute the known values

Substitute \(a = 15\) and \(c = 17\) into the Pythagorean theorem: \(15^{2}+x^{2}=17^{2}\). Calculate \(15^{2}=225\) and \(17^{2}=289\). So the equation becomes \(225+x^{2}=289\).

Step3: Solve for \(x\)

Subtract 225 from both sides of the equation: \(x^{2}=289 - 225\). \(289-225 = 64\). Then take the square root of both sides: \(x=\sqrt{64}=8\) (we take the positive square root since distance cannot be negative).

Answer:

8