The height BD of triangle ABC divides its side AC into segments AD and CD.

The height BD of triangle ABC divides its side AC into segments AD and CD. Find the length of the segment CD, if AB = 2√3 (cm), BC = 7 (cm), angle A = 60 degrees.

The height BD forms two right-angled triangles ABD and BCD.

In a right-angled triangle ABD, the value of the angle ABD = (180 – 90 – 60) = 30, then the leg AD, which lies opposite this angle, is equal to half of the hypotenuse AB.

АD = 2 * √3 / 2 = √3 cm.

Then, by the Pythagorean theorem, BD ^ 2 = AB ^ 2 – AD ^ 2 = 12 – 3 = 9.

ВD = 3 cm.

In a right-angled triangle BCD, according to the Pythagorean theorem, we determine the length of the leg CD.

CD ^ 2 = BC ^ 2 – BD ^ 2 = 49 – 9 = 40.

СD = √40 = 2 * √10 cm.

Answer: The length of the CD segment is 2 * √10 cm.