two forces of magnitudes 7N and 9N act at an angle alpha such that sin alpha=0.4. Find the magnitudes of the two possible resultants

Answer 1

If we let one force be
(7,0) then the other is (9cosθ,9sinθ) where sinθ = 0.4

cosθ = ±0.92

(7,0)+(8.25,3.6) = (15.25,3.6)
(7,0)+(-8.25,3.6) = (-1.25,3.6)

The magnitudes are 15.67 and 3.81

Answer 2

(cscalpha -1)(cscalpha +1)=cot^(2)alpha