# Two bodies are projected at angle theta and 90 minus theta to the horizontal with the same speed the ratio of their horizontal ranges are?

$1 : 1$
Formula for range of a projectile is $R = \frac{{u}^{2} \sin 2 \theta}{g}$ where,$u$ is the velocity of projection and $\theta$ is the angle of projection.
For,$u$ be the same for both the bodies,
${R}_{1} : {R}_{2} = \sin 2 \theta : \sin 2 \left(90 - \theta\right) = \sin 2 \theta : \sin \left(180 - 2 \theta\right) = \sin 2 \theta : \sin 2 \theta = 1 : 1$ (as, $\sin \left(180 - 2 \theta\right) = \sin 2 \theta$)