Using the following formulas:
Range = [ Vo^2 sin 2theta ]/g
Height = [ Vo^2 sin theta^2 ]/g
Since the relation between Range and height is given: ( R = 3H ), the 2 equations can be equated in terms of Vo^2 so that the only remaining unknown variable left will be the angle. This is done as shown:
( gRange )/(sin 2theta) = Vo^2
( gHeight )/(sin theta^2) = Vo^2
( gRange )/(sin 2theta) = ( gHeight )/(sin theta^2)
Applying Range = 3Height:
( g3Height )/(sin 2theta) = ( gHeight )/(sin theta^2)
substituting given values while Height cancels out:
( 9.83 )/(sin 2theta) = ( 9.8 )/(sin theta^2)
Angle theta = 33.67 degrees
