Find the area of an isosceles triangle if its height is 5 * 4√3 / 2 and the apex angle is 120 degrees?

univerkov | June 2, 2021 | education

Since triangle ABC is isosceles, its height BH is also its median and bisector. Then AH = CH = AC / 2, angle ABH = ABC / 2 = 120/2 = 60.

Triangle ABH is rectangular, in which tgABH = AH / BH.

AH = BH * tg60 = 5 * 4 * √ (3/2) * √3 = 60 / √2 = 30 * √2 cm.

Then AC = 2 * AH = 60 * √2 cm.

Sаvs = АС * ВН / 2 = 60 * √2 * 5 * 4 * √ (3/2) / 2 = 600 * √3 cm2.

Answer: The area of the triangle is 600 * √3 cm2.

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