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

CoolStuffYT Nov 4, 2018

#1**+3 **

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>>>>!!!!

CPhill Nov 4, 2018

#2**+3 **

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°**

Dimitristhym
Nov 4, 2018