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Altitudes AX and BY of acute triangle ABC intersect at H. If angle BAC = 43 degrees and angle ABC = 67 degrees, then what is angle AHC?

 Apr 19, 2021
 #1
avatar+108 
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"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°"

 

WORDS OF CPhill

 Apr 19, 2021
 #2
avatar+118505 
+1

YHXB  is  a  quadrilateral

Angles HYB  and HXB  = 90

Angle YBX =  67

 

So angle  YHX  = 360  -67  - 90  - 90 =     180  - 67  =  113°

 

And angle AHC  is a vertical angle  to YHX  so it  has  the  same measure   = 113°

 

 

cool cool cool

 Apr 19, 2021

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