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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
avatar+91360 
+2

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>>>>!!!!

 

cool cool cool

CPhill  Nov 4, 2018
edited by CPhill  Nov 4, 2018
 #2
avatar+316 
+2

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
edited by Dimitristhym  Nov 4, 2018
edited by Dimitristhym  Nov 4, 2018
 #3
avatar+91360 
+1

Oops!!!....just a typo.....you are correct!!!

 

I have fixed it....

 

cool cool cool

CPhill  Nov 4, 2018
edited by CPhill  Nov 4, 2018
 #4
avatar+116 
+1

Thanks!

CoolStuffYT  Nov 6, 2018

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