First of all, get the VERTICAL component of the initial velocity:
V = 37m/s (sin(44.9) = 26.117 m/s
When the Vertical velocity equals ZERO, the projectile has reached its highest point (apex)
since v= vo + at (vo = origianl velocity a = acceleration of gravity = -9.80 m /sec^2 t = time)
ZERO= 26.117 + (-9.80 t)
Solving for t
-26.117 = -9.8 t
26.117/9.8 = t = 2.665 seconds
NOW, use the position equation pf = po + vt +1/2at^2 pf=Final position (max height...apex)
po = 0
so:
pf = 26.117 (2.665) + 1/2 (-9.8)(2.665)^2 = 69.60 + (-34.8) = 34.8 m max height
CORRECTED MATH ERROR IN LAST LINE