Part 1: An airplane ﬂies 221 km due west from city A to city B and then 387 km in the direction of 25.5 degrees north of west from city B to city C. What is the distance between city A and city C?
Answer in units of km
Part 2: Relative to city A, in what direction is city C? Answer with respect to due east, with the
counter-clockwise direction positive, within the limits of −180 degrees to +180 degrees.
Answer in units of degrees
From the theorem of cosines we get for triangle ABC: AB^2+BC^2-ABBCcos(B)=AC. After putting numbers we get answer. 479 km.
If we take BC as hypotenuse of triangle ABH with angle H=90, then BC*sin(180-115)=CH CH will be leg of triangle ACH, where we don't know angle A, but when we use definition of tangents, we will get AB+BH=Ab+BC*Cos(180-115) and AC known from the task. Arctg(AC/(AB+BH) gives us 42.7 degrees If we calculate due to east, it will be 137.2 degrees.