For angles of projection of a projectile at angles 45∘−θ and 45∘+θ, the horizontal range described by the projectile are in the ratio of

Horizontal range, R=u2sin⁡2θgFor angle of projection 45∘−θ, the horizontal range is :R1=u2sin⁡245∘−θg=R1=u2sin⁡90∘−2θg=u2cos⁡2θgFor angle of projection 45∘+θ, the horizontal range is :R2=u2sin⁡245∘+θg=u2sin⁡90∘+2θg=u2cos⁡2θg∴R1R2=u2cos⁡2θ/gu2cos⁡2θ/g=11.