# How do you solve the triangle given A=36, a=10, b=19?

Mar 29, 2018

There is no triangle possible with these measures.

#### Explanation:

$\sin \frac{{36}^{\circ}}{10} = \sin \frac{B}{19}$
$\sin \left(B\right) = \frac{19}{10} \cdot \sin \left({36}^{\circ}\right) = 1.9 \cdot \sqrt{\frac{5 - \sqrt{5}}{8}} \approx 1.1168$
But we know that this is impossible because $\sin \left(B\right)$ must be less than or equal to 1, so we cannot construct a triangle with these measures.