Question

A train leaves train station A and heads due west for 105 miles to reach train station B. Another train leaves train station A at the same time and travels 85 miles to train station C in a direction 45 north of west from station A. To the nearest mile, how far is train station C from train station B? 75 miles 109 miles 135 miles 176 miles

Answer 1

135 Miles

Explanation:

Answer 2

At the nearest mile, stations B and C are 75 miles apart.

Explanation:

In the attached image we can see all the three stations. The closest distance between stations B and C would be a straight line that can be calculate using the Cosine Rule:

`(BC)^2=(AB)^2+(AC)^2-2(AB)(BC)cos(\alpha)`}

Where:

AB is the distance between stations A and B

AC is the distance between stations A and C

α is the angle formed between the AC and AB railway lines

`(BC)^2=(105)^2+(85)^2-2(105)(85)cos(45)`

`BC=75.02 miles`

So, at the nearest mile, stations B and C are 75 miles apart.