If you remember the following formula : H / R = tan Ф / 4 , then its quick.
H = R => Ф = tan⁻¹ 4.
In two dimensional projection of a particle in Earth's gravitational field, we have the following equations :
x = u Cos Ф * t --- (3)
y = u Sin Ф * t - 1/2 g t² --- (1)
v_x = velocity in horizontal direction : u * cosФ
v_y = vertical velocity upwards = u SinФ - g t
v_y = 0 at t = u SinФ/ g
Then by (1) above, y at t = u SinФ/ g is equal to = H
H = u² Sin²Ф /2g ---(2)
In the time duration t = u SinФ/g, the projectile travels, a distance of half the Range. Using (3) we get :
R/2 = u² CosФ SinФ / g
R = u² Sin2Ф / g -- (4)
From (2) and (4) we get :
H / R = Tan Ф / 4 ---- (5)
If H = R are equal, then the angle of projection = tan⁻¹ 4 = 75.96 deg.
sin A = 4 cos A
Sin² A = 16 Cos² A
cos² A = 1/17
Cos A = 1/√17
Sin A = 4/√17