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Altitudes AD and BE of triangle ABC intersect at H.  If BAC = 54 and ABC = 56, then what is angle AHB?

 Dec 18, 2021
 #1
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1)  Knowing the sizes of angles BAC and ABC, you can find the size of angle ABC.

 

2)  In quadrilateral ECDH, you know the sizes of angles ACB, CEH and CDH; so, you can find the size of angle EHD.

 

3)  Knowing the size of angle EHD, you can find the size of angle AHB.

 Dec 18, 2021
 #2
avatar+13021 
+1

 What is angle AHB?

 

Hello Guest!

 

The sides AC and BC are lines in the right-angled coordinate system.

\(m_{h_a}=-\frac{1}{tan(-56°)}\\ \angle HAB=atan\ m_{h_a}=\color{blue}34°\)

\(m_{h_b}=-\frac{1}{tan(54°)}\\ \angle ABH=atan\ m_{h_b}=\color{blue}-36°\)

\(\angle AHB=180°-34°-36°\)

\(\angle AHB=110°\)

laugh  !

 Dec 18, 2021
edited by asinus  Dec 18, 2021
edited by asinus  Dec 18, 2021
edited by asinus  Dec 18, 2021

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