Question

A shot is fired at an angle theta to the horizontal up a hill of inclination sin^-1 (4/5) to the horizontal. If the shot strikes the hill horizontally, then the value of theta is.

Answer 1

by sin^-1 = 4/5 you can conclude that height of hill is 4 units and distance between observer and hill is 3units. as shot strikes horizontallly it means vertical component should be zero.
so it strikes at maximum height.
maximum height = 4 units
range = 3+3 = 6 units
now , using height / range = tanx /4 where x is the theta I let.
so tanx = 16/6 = 8/3
so x = tan^-1 8/3