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 1 mile. if the two cars are now a straight - line distance of 2.1 miles apart, how far has the northbound car traveled? if necessary, round to the nearest tenth. miles

Explanation:

Step1: Apply Pythagorean theorem

Let the distance of the north - bound car be \(x\) miles. The east - bound car's distance \(a = 1\) mile and the straight - line distance \(c=2.1\) miles. By the Pythagorean theorem \(a^{2}+x^{2}=c^{2}\), so \(x^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 1\) and \(c = 2.1\) into the equation: \(x^{2}=(2.1)^{2}-1^{2}\).
Calculate \((2.1)^{2}=4.41\) and \(1^{2}=1\). Then \(x^{2}=4.41 - 1=3.41\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{3.41}\approx1.8\) (rounded to the nearest tenth).

Answer:

\(1.8\)