Find CD and AD. Angle A = 30 degrees, Angle B = 90 degrees. AC = 12 cm

The BC leg lies against an angle of 30, then BC = AC / 2 = 12/2 = 6 cm.

By the Pythagorean theorem, in a right-angled triangle ABC, AB ^ 2 = AC ^ 2 – BC ^ 2 = 144 – 36 = 108.

AB = 6 * √3 cm.

In a right-angled triangle ABD, leg BD lies opposite angle 30, then BD = AB / 2 = 6 * √3 / 2 = 3 * √3 cm.

By the Pythagorean theorem, in a right-angled triangle ABD, AD ^ 2 = AB ^ 2 – BD ^ 2 = 108 – 27 = 81.

AD = 9 cm, then CD = AC – AD = 12 – 9 = 3 cm.

Answer: The length of the segment АD = 9 cm, СD = 3 cm.




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