In triangle ABC, the angles of which are ∠B = 40∘ and ∠C = 80∘, the height CH is drawn. Find the ACH angle (in degrees).

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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