The angle at the apex of an isosceles triangle is 120 °. a) Let its side be equal to 1.

| June 23, 2021 | education

The angle at the apex of an isosceles triangle is 120 °. a) Let its side be equal to 1. Calculate the base. b) let its base be equal to 1. Calculate the side

From the top of the obtuse angle B, we draw the height BH, which, in an isosceles triangle, also has a bisector and a median.

Then the angle ABH = CBH = ABC / 2 = 120/2 = 600, and AH = CH = AC / 2.

Angle BAC = 180 – 90 – 60 = 30.

If AB = BC = 1 cm, then in a right-angled triangle ABH SinABH = AH / AB.

AH = AB * Sin60 = 1 * √3 / 2 = √3 / 2 cm.

Then AC = AH * 2 = 2 * √3 / 2 = √3 cm.

Answer: The length of the base is √3 cm.

If AC = 1, then AH = AC / 2 = 1/2 cm.

Then in a right-angled triangle ABH SinABH = AH / AB.

AB = AH / SinABH = (1/2) / (√3 / 2) = 1 / √3 cm.

Answer: The length of the side is 1 / √3 cm.



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