Interpolate between 2 impact points only given the throw angles

[Werther]

Homework Statement

A cannon shoots at target P1 and P2 with the given vertical/horizontal angles (α/b). But there is a third target (P3) left that is between P1 and P2. Unfortunately the soldier that shoots the cannon only knows the vertical angle (a3=65°) and not the horizontal angle. Notice that the velocity of the projectile and the position of the impact points are unknown.

What is the horizontal angle for shooting at P3 (b3)?

Relevant Equations

projectile velocity:
Vx = cos b * Vc
Vy = sin b * Vc

impact location:
x = Vx*t

Top-Down-Perspective:

At first I am quite sure that the problem is not solvable since there are that many unknowns.
But my Approach would be to create a linear function with P1 and P2 and then set it equal to the function that gets me the impact location of P3 and then solve it by b3.

Thanks for the help in advance.

 

[PeroK]

What are "horizontal" and "vertical" angles?

 

[Werther]

What are "horizontal" and "vertical" angles?

horizontal = tilt of the cannon
vertical = rotating the cannon left or right

 

[PeroK]

Okay, and how is P3 related to P1 and P2?

 

[haruspex]

horizontal = tilt of the cannon
vertical = rotating the cannon left or right

Really? Sounds backwards to me, but from the values given that must be right.

"that is between P1 and P2"
Merely somewhere between, or on the straight line joining them?

 

[Werther]

Okay, and how is P3 related to P1 and P2?

P3 sits in the line If you would draw one through P1 and P2.

 

[haruspex]

Let the muzzle velocity be v.
Write expressions for the target coordinates in terms of v and the two angles.