Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?
Draw altitude CG (it will also pass through H)
Angle ABH = 30
Angle CBG = 30
Angle CGB = 90
So angle GHB = 60
So angle EHC = 60
And angle HEC =90
So angle HCA = 180 - 60 - 90 = 180 - 120 = 30
+380 
