Projectile A - > B , two different angles

[lax1113]

Homework Statement

Muzzle velocity at A = Vo. Determine the two angles, theta 1 and theta 2.

A is separated from B by a distance L in the x direction and a height H. (B is on a hill above A).

Homework Equations

The Attempt at a Solution

I feel that the important facts of this problem is that sin(theta1)Vo * t1 - gt1^2 = sin ( theta2 )Vo * t2 - gt2^2, since the y displacement for both projectiles are identical. Similarly, we have that the x projectiles are the same, so that cos (theta1 )Vo * t1 = cos ( theta 2 )Vo * t2.
With these equations, I have two variables two equations, but I cannot figure out how/if it is possible to solve these to isolate a variable. I am guessing that there is probably an easier way to do this, so a small hint would be greatly appreciated!

thanks guys.

 

[lax1113]

Actually, after a bit more working through, I came up with a quadratic in terms of tan ( theta ) . The equation itself looks pretty nasty, but does this make sense? I have a tan^2, Tan, and then a constant, so it seems like it could definelty be a quadratic.

Any input apprecaited.