Triangle

Question

+1

457

2

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?

Guest Apr 19, 2021

XxMysteriousGirlxX · Answer 1 · 2021-04-19T09:54:25

"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

CPhill · Answer 2 · 2021-04-19T10:12:19

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°