The bearing shows the angle from north to the line (c), you want to see the angle inside the triangle so that will be 90-[bearing].
a=42 (42 mph wind blowing north)
A= 90-74.9
A= 15.1 degrees
Ground speed is the speed the plane is going including the wind.
ground speed = c
Airspeed = b
You have the angle, and you have the "Opposite" and want to find the "Hypotenuse".
SOH CAH TOA
Sin x = Opp/Hypot
Sin(15.1) = 42/c
c = 42/Sin(15.1)
c = 161.53
Ground speed of the plane is 161.53 mph
Airspeed = b
Tan x = Opp/Adj
Tan (15.1) = 42/b
b = 42/Tan(15.1)
b = 161.53
Airspeed = 161.53 mph
(so the answer is ground speed of 161.53mph)
