[ام عبد الرحمن محمد]

(a) Range of a projectile is given by
R = (u^2 sin 2θ) / g
The maximum height is given by
H = (u^2 sin^2 θ) / 2g

Here R = H
Simplify to get
sin 2θ = sin^2 θ / 2
Put sin 2θ = 2 sin θ cos θ
So
4 cos θ = sin θ
or tan θ = 4

θ = tan^-1 (4) = 76 °

(b) The answer does not depend on acceleration due to gravity (g); it cancels out in the beginning. So the answer would be same even on another planet.

(c) R = (u^2 sin 2θ) / g
Greater the value of sin 2θ, greater the range.
sin 2θ lies between -1 and 1.
So maximum value of sin 2θ = 1.
When sin 2θ = 1,
2θ = 90
or θ = 45

Put sin 2θ = 1 in the expression for Range :
R = u^2 / g