Projectile motion is characterized by a motion that has two vector forces: the velocity along the x and y directions. As a result, the motion follows an arc-shaped direction. These two directions are actually independent of each other.
There are already derived equations for this so it is already convenient. However, your given equation for range is incomplete. The correct equation is:
R = v₀²sin2θ/g
where
R = 140 ft
v₀ = 120 ft/s
g = 32.2 m/s²
Substituting the values,
sin 2θ = Rg/v₀²
sin 2θ = (140)(32.2)/(120²)
sin 2θ = 0.313
2θ = sin ⁻¹ (0.313)
2θ = 18.24°
θ =18.24°/2
θ = 9.12°
