From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles

Question

Masteriza [31]

2 years ago

14

From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles

, and the eastbound train has traveled 16 miles. How far apart are the two trains, measured in a straight line?

Mathematics

1 answer:

tigry1 [53] · Answer 1 · 2022-09-18T13:03:10+03:00

9514 1404 393

Answer:

20 miles

Step-by-step explanation:

The north and east distances form the legs of a right triangle. The straight-line distance between the trains is the hypotenuse of that triangle. The Pythagorean theorem can be used to find the length of the hypotenuse (d).

d² = 12² +16²

d² = 144 +256 = 400

d = √400 = 20

The two trains are 20 miles apart.

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<em>Additional comment</em>

You may recognize the given distances are in the ratio 3 : 4. You may recall that side ratios of 3 : 4 : 5 make a right triangle. If so, you recognize that the straight-line distance is (4 miles)×5 = 20 miles. (3:4:5 right triangles show up often in algebra and geometry problems, so might be something you want to look for.)