The medians AA1, and CC1 of the isosceles triangle ABC with the base AC intersect at point O

| September 11, 2021 | education

The medians AA1, and CC1 of the isosceles triangle ABC with the base AC intersect at point O. It is known that the angle AOC = 100 °, AA1 = 3 cm. Calculate the length of the lateral side of the triangle ABC.

Since the ABC triangle is isosceles, its medians drawn to the lateral sides are equal, AA1 = CC1 = 3 cm.

The medians of a triangle are divided at the intersection point by a ratio of 2/1, starting at the apex.

Then OA1 = OC1 = 1 cm, OA = OC = 2 cm.

The COA1 angle is adjacent to the AOC angle, then the COA1 angle = (180 – 100) = 80.

In the triangle СОА1, by the cosine theorem:

CA1 ^ 2 = OA1 ^ 2 + OS ^ 2 – 2 * OA1 * OS * Cos80 = 1 + 4 – 2 * 1 * 2 * 0.173 = 4.305 cm.

CA1 = 2.075 cm.

Then BC = 2 * CA1 = 4.15 cm.

Answer: The length of the side is 4.15 cm.



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