In triangle ABC, angles A and C are equal, AC = 16cm, the bisector of angle B is 15cm. Find BC.

univerkov | February 4, 2021 | education

Since, by condition, the angle BAC = BCA, the triangle ABC is isosceles with the base of the AC.

Then, the bisector of the angle ABC will also be the height and median of the triangle ABC, which means that the triangle BCH is rectangular, and CH = AH = AC / 2 = 16/2 = 8 cm.

We use the Pythagorean theorem and determine the length of the BC hypotenuse.

BC2 = BH2 + CH2 = 225 + 64 = 289.

BC = 17 cm.

Answer: The length of the BC side is 17 cm.

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