Trigonometric Expression for Side c

Very Hard Additional Topics In Math Trigonometry

In triangle ABC, angle A measures 30 degrees, and side a measures 10 units. The altitude from point A to side BC meets BC at point D. If the length of side c (the side opposite angle C) is expressed in terms of $b$, the side opposite angle B, which is unknown, which of the following expressions is the correct representation for $c$?

$$c = b \cos(30^\circ)$$

$$c = b + 10 \sin(30^\circ)$$

$$c = \frac{10 \sin(B)}{\sin(30^\circ)}$$

$$c = \frac{10 \sin(60^\circ)}{\sin(B)}$$

Hint

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