I assume this refers to a trajectory problem?
Neglecting complicating factors such as air resistance, we launch an object with speed #v# at an angle #theta# to the ground, where #y# is our vertical axis. The initial vertical component of its velocity is then #v sin theta#, using trigonometric components.
It is subject to a downward acceleration #g# due to gravity. Acceleration is the rate of change of velocity, and so the vertical velocity as a function of time is #int -g dt = C - g t #, where #C# is a constant of integration, to be determined from given information. The relevant piece of information is the initial vertical velocity - when #t=0#, #v_y=v sin theta#, and so #v sin theta = C - g*0 = C#. Thus #v_y(t) = v sin theta - g t #, the vertical velocity as a function of time.
Now the moment of maximum height happens when the object stops rising - when #v_y(t)=0#. Setting this, #v sin theta - g t = 0#, which we solve for #t#, answering the question:
#t = v/g sin theta#
