Maximum Range R = \(\frac{u^2sin2\theta}{g}\) maximum height H = \(\frac{u^2sin^2\theta}{2g}\) But R : H = 4 \(\frac{u^2sin2\theta}{g}\) : \(\frac{u^2sin^2\theta}{2g}\) = 4 \(\frac{u^2sin2\theta}{g} \times\frac{2g}{u^2sin^2\theta}\) = 4 \(\frac{2sin2\theta}{sin^2\theta}\) = 4 since 2sinΘ = 2sinΘcosΘ \(\frac{2 \times 2sin\theta cos\theta}{sin^2\theta}\) = 4 \(\frac{4sin\theta cos\theta}{sin^2\theta}\) = 4 \(\frac{sin\theta cos\theta}{sin^2\theta}\) = 1 \(\frac{cos\theta}{sin\theta}\) = 1 \(\frac{sin\theta}{cos\theta}\) = 1 \(tan \theta\) = 1 \(\theta = tan^{-1}1\) = 45^\circ