In a right triangle ABC, \angle A=90^\circ and AD is perpendicular to BC. If \angle CAD=60^\circ and BC=6 cm, then what is AB equal to?

Explanation

In right \triangle ABC, \angle A = 90^\circ. Since AD \perp BC and \angle CAD = 60^\circ, the remaining angle in \triangle ADC is \angle C = 30^\circ. For the large triangle ABC, AB = BC \sin(\angle C) = 6 \sin 30^\circ = 6 \times \frac{1}{2} = 3 cm.

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