The height drawn to the base of the AC in the isosceles triangle ABC is 8.7 cm, and the lateral side of this triangle is 17.4 cm. Find all the angles.
The height BH divides the isosceles triangle ABC into two equal right-angled triangles ABH and BCH.
In a right-angled triangle ABH, the length of the BH leg is half the hypotenuse AB, then the angle against the BH leg is 30, and therefore the angle BCH = BAC = 30.
Then the angle ABC = (180 – BCH – BAC) = (180 – 30 – 30) = 120.
Answer: The angles of the triangle ABC are 30, 30, 120.
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