# In triangle ABC, height AD divides side BC into segments BD = 4√3cm and DC = 16cm. Angle ABC = 60 °. Find AB and AC.

July 22, 2021 | education

| Since AD is height, triangles ABD and ACD are rectangular.

In a right-angled triangle ABD, the angle BAD = (90 – 60) = 30, then its leg BD, which lies opposite the hypotenuse AB, is equal to half its length. Then AB = 2 * BD = 2 * 4 * √3 = 8 * √3 cm.

By the Pythagorean theorem, AD ^ 2 = AB ^ 2 – BD ^ 2 = 192 – 48 = 144.

AD = 12 cm.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 144 + 256 = 40.

AC = 20 cm.

Answer: The length of the AB side is 8 * √3 cm, the AC side is 20 cm.

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