Question

from a train station, one train heads north, and another heads east. some time later, the northbound train has traveled 33 kilometers, and the eastbound train has traveled 44 kilometers. how far apart are the two trains, measured in a straight line? kilometers

Explanation:

Step1: Identify the triangle type

The paths of the two trains (north and east) and the straight - line distance between them form a right - triangle. The two legs of the right - triangle are the distances traveled by the north - bound train (\(a = 33\) km) and the east - bound train (\(b = 44\) km), and the hypotenuse (\(c\)) is the straight - line distance between the two trains.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\).

Substitute \(a = 33\) and \(b = 44\) into the formula:

First, calculate \(a^{2}\) and \(b^{2}\):
\(a^{2}=33^{2}=33\times33 = 1089\)
\(b^{2}=44^{2}=44\times44 = 1936\)

Then, calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=1089 + 1936=3025\)

Finally, calculate \(c\):
\(c=\sqrt{3025}=55\)

Answer:

55