In an isosceles triangle ABC with a base AC = 24cm, median BD = 5cm Find: a) lateral sides b) cos A.

univerkov | February 9, 2021 | education

Since the triangle ABC is isosceles, the median of the ВD is also the height of the triangle, and then the triangles AВD and ВСD are rectangular.

We divide the median СD into two equal segments. AD = СD = AC / 2 = 24/2 = 12 cm.

According to the Pythagorean theorem, in the AВD triangle, we determine the length of the hypotenuse AB.

AB ^ 2 = AD ^ 2 + ВD ^ 2 = 144 + 25 = 169.

AB = BC = 13 cm.

Let us determine the cosine of the angle A, which is the ratio of the AD adjacent to the angle to the hypotenuse AB.

CosA = AD / AB = 12/13.

Answer: The sides of the triangle are 13 cm, CosA = 12/13.

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