In a triangle ABC AC = 10, AB = BC, cos C = 0.8, CH is the height. Find AH

Since, according to the condition, AB = BC, then the triangle ABC is isosceles with the base AC, then the angle BAC = BCA, which means CosBAC = CosBCA = 0.8.

The SAN triangle is rectangular, since CH is the height, then CosCAH = AH / AC.

AH = AC CosCAH = 10 * 0.8 = 8 cm.

Answer: The length of the segment AH is 8 cm.

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