Let’s find the angle A, knowing the angles B and C:
∠А = ∠НАС = 180º – (∠В + ∠С) = 180º – (40º + 80º) = 60º.
Consider the AСН triangle.
It is rectangular with a right angle CHA, since CH is the height of the triangle ABC from the vertex C.
Then, knowing the angle CHA and the angle HAC, we find the angle ACH.
∠АСН = 180º – (∠СНА + ∠HАС) = 180º – (90º + 60º) = 180º – 150º = 30º.
Answer: ∠АСН = 30º.
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