In triangle ABC AB = BC angle CAB = 30 bisector BE = 8, find area.

univerkov | July 28, 2021 | education

Since AB = BC, the triangle ABC is isosceles, and then its bisector BE is also the height and median of the triangle. Then the triangles ABE and CBE are rectangular.

In a right-angled triangle ABE tg30 = BE / AE.

AE = BE / tg30 = 8 / (√3 / 3) = 16 / √3 = 24 * √3 / 3 = 8 * √3.

Then AC = 2 * AE = 2 * 6 * √3 = 16 * √3 cm.

Determine the area of the triangle.

Savs = AC * BE / 2 = (16 * √3 / 2) * 8 = 64 * √3 cm2.

Answer: The area of the triangle is 64 * √3 cm2.

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