Gordon and Brian leave a hostel at the same time Gorden walk

Gordon and Brian leave a hostel at the same time. Gorden walks on a bearing of 045 degree at a speed of 4.4 kilometres per hour. Brian walks on a bearing of 100 degree at a speed of 4.8 kilometres per hour. If they both walk at stead speed, how far apart will they be after 2 hours?

Solution

the angle between gordon and brian = 100 - 45 = 55 degrees

distance covered by brian after 2 hours = 4.8* 2 = 9.6

distance covered by gordon after 2 hours = 4.4* 2 = 8.8

applying coine rule to find the distance between brian and gordon

BG^2 = 8.8^2 + 9.6^2 - 2*8.8*9.6 cos 55

BG^2 = 164.41 - 96.91

BG = 8.5 kilometres

distance between brian and gordon after 2 hours = 8.5 kilometres