# How do you solve the triangle given A=30*, a=3, b=8?

Aug 20, 2015

There is no triangle having these measurements.

#### Explanation:

The Law of Sines tells us that we would have:

$\sin \frac{B}{8} = \sin {30}^{\circ} / 3$

We know that $\sin {30}^{\circ} = \frac{1}{2}$ so we get:

$\sin B = \frac{8 \left(\frac{1}{2}\right)}{3} = \frac{4}{3}$

There is no angle whose sine is $\frac{4}{3}$ so there is no triangle that has these measurements.