Plzzzzzzzz help me plzzzz

Dear Student,

v_rain,road = v_rain,man + v_man,road ….................. (1)

Taking horizontal components in the equation (1) along the line OA [from figure a],

v_rain,road sin(α) = 8 …......................(2)

From figure b we have,

v_rain,road sin(30 + α) = 12 cos30 …................(3)

Now,

(3)/(2)=> [sin(30 + α)]/sin(α) = [12 cos30]/8

Solving this equation we get,

tan α = 1.154

=> α = 49⁰

Using (2),

v_rain,roadsin(49) = 8

=>v_rain,road= 8/0.75

=>v_rain,road= 10.6 m/s

Regards