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# Triangles

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60
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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
+22572
+1

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
+13021
+1

What is angle AHB?

Hello Guest!

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

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

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

$$\angle AHB=180°-34°-36°$$

$$\angle AHB=110°$$

!

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