Answer:
Option (a) is correct.
To the nearest mile, the distance between train station C from train station B is 75 miles.
Step-by-step explanation:
Given : 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.
We have to find the distance between train station C from train station B.
We first draw the position of stations according to given statement.
Figure shown below in attachment.
Since we have to find the distance BC , Let BC = x
For a triangle ABC, with ∠A = 45° and AB = 105 m and AC = 85 m
Using Cosine rule,
\(BC=\sqrt{CA^2+AB^2-2\cdot AB\cdot AC\cdot \cos A }\)
Substitute, we have,
\(x=\sqrt{(85)^2+(105)^2-2\cdot 85\cdot 105\cdot \cos 45^{\circ}}\)
Simplify , we have,
\(x=75.020\)
Thus, to the nearest mile, the distance between train station C from train station B is 75 miles.
