Question

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?

Answer 1

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°