The angle α to the target top is measured from the eye level line of the observer to the top of the nearest target. If the target top is below eye level, the angle is negative, else positive.

Note: this equation is robust and gives positive and negative angles α correctly without the need of handling multiple cases.

Derivation

We know R, T, Z and D. From this we can calculate a = a₁ + a₂ = R + Z, b = R + T and γ = D / R.

In the first step I calculate h using Pythagoras:

Combining this 2 equations we can eliminate h² and solve for c²:

We can calculate a₂ using trigonometry and a₁ = a − a₂:

We can insert (7) into (5) to get c with all values known:

Our unknown drop angle is according to trigonometry α = −asin( a₁ / c ). Now we have all we need to calculate the target top angle α: