+1253 Altitudes AX and BY of acute triangle ABC intersect at H. If angle BAC = 43 and angle ABC = 67, then what is the angle HCA?
Thank You :P
+128448 Angle BAC = angle ZAC = 43°
Angle CZA = angle CZB = 90°
So triangle ZAC is a right triangle and angle ZCA is complementary to angle ZAC = 47°
And angle ZCA = angle HCA = 47°
EDIT TO CORRECT AN ERROR>>>>!!!!
+343 CPhill I think you have a mistake,all it's right but in the end it's
angle ZCA = angle HCA = 47° NOT 43°
because :
angle CZA + angle ZAC + angle ZCA = 180° in triangle ZAC
so 43° + 90° + angle ZCA = 180°
so angle ZCA = 180°-133° = 47°
So angle ZCA = angle HCA = 47°
