To a cyclist riding west at 20 kg/hr, the rain appears to meet him at an angle of 45° with the vertical. When he rides at 12 km/hr, the rain meets him at an angle of 19°48' with the vertical. What is the actual direction of the rain?

Get the angle between the vertical and the line of sight of the cyclist parallel to the rain at 19°48’

180 - 90 - 19°48’ = 70.2 °

Prepare two equations to solve for the velocity of the rain

DC2 sin 70.2 = (12 - x) tan 70.2

DC1 tan 45 = (20 - x) tan 45

Solving the equation results to

x = 3.8

and

RD = 14.20

The actual angle of the rain is,

90 - tan-1 (14.20/3.8) = 15°