A triangle has angles of 30° and 45°. If the side opposite the 45° angle has length 8, then the side opposite the 30° angle has length:

1972 AMC 12 Problem 14

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14.

A triangle has angles of

30^\circ

and

45^\circ.

If the side opposite the

45^\circ

angle has length

8,

then the side opposite the

30^\circ

angle has length:

4

4\sqrt2

4\sqrt3

4\sqrt6

6

Relate the two sides with the Law of Sines

Use

\sin30^\circ=\frac{1}{2}

and

\sin45^\circ=\frac{\sqrt2}{2}

s

is the side opposite

30^\circ,

the Law of Sines gives

\frac{s}{\sin30^\circ}=\frac8{\sin45^\circ}.

Therefore

s=8\frac{\frac{1}{2}}{\frac{\sqrt2}{2}}=4\sqrt2.

Therefore, the correct answer is B.