Height AD divides side BC of triangle ABC into segments BD and DC Find sides of triangle ABC

| August 12, 2021 | education

Height AD divides side BC of triangle ABC into segments BD and DC Find sides of triangle ABC if AD = 6 cm ABC = 45 degrees ACB = 60 degrees.

From the right-angled triangle ACD, through the leg AD and the angle CAD, we determine the hypotenuse of the AC and the leg CD.

Singad = AD / AC.

AC = AD / Sing.

AC = 6 / (√3 / 2) = 12 / √3 = 4 * √3 cm.

tgsad = AD / CD.

СD = АD / tgсad = 6 / tg60 * 6 = 6 / √3 = 2 * √3 cm.

In a right-angled triangle ABD, the angle ADB is straight, and the angle ABD is 45, then the angle BAD = 180 – 90 – 45 = 45, and the triangle ABD is isosceles, AD = BD = 6 cm.

Then Side AB = √62 + 62 = √72 = 6 * √2 cm.

Let us determine the length of the BC side. ВС = ВD + СD = 6 + 2 * √3 cm.

Answer: AC = 4 * √3 cm, AB = 6 * √2 cm, BC = 6 + 2 * √3 cm.



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