The height BD of triangle ABC divides its side AC into segments AD and CD, find CD if AB = 2√3

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

For a triangle ABC, sides AB = 2√3 cm; BC = 7 cm; <A = 60 °. The height BD divides the AC side into AD. and DC. Let’s calculate <ABD = 90 ° – 60 ° = 30 °.

Then AD = 2√3 / 2 = √3 (cm), as a leg, lying opposite the angle <ABD = 30 °. We define ВD = √ [(AB ^ 2 – АD ^ 2)] = √ [(2√3) ^ 2 – (√3) ^ 2] = √ (12 – 3) = √9 = 3 (cm).

Let’s define СD = √ [(ВС) ^ 2 – (ВD) ^ 2] = √ [7 ^ 2 – 3 ^ 2] = √ [49 – 9] = √ [40] = 2 * √10.

Answer: СD = 2 * √10.