How do you solve the triangle given A=25, B=78, a=13.7?

Jan 5, 2017

$\left(\angle A , \angle B , \angle C\right) = \left({25}^{\circ} , {78}^{\circ} , {77}^{\circ}\right)$
$\left(a , b , c\right) = \left(13.7 , 31.71 , 31.59\right)$
$\textcolor{w h i t e}{\text{XXX}}$($b$ and $c$ are approximate)

Explanation:

If $\angle A = {25}^{\circ}$
and $\angle B = {78}^{\circ}$
then
$\textcolor{w h i t e}{\text{XXX}} \angle C = {180}^{\circ} - \left({25}^{\circ} + {78}^{\circ}\right) = {77}^{\circ}$

Given $a = 13.7$ and using the Law of Sines
$\textcolor{w h i t e}{\text{XXX}} b = \frac{a}{\sin \left(\angle A\right)} \cdot \sin \left(\angle B\right) \approx 31.7085733$
and
$\textcolor{w h i t e}{\text{XXX}} c = \frac{a}{\sin \left(\angle A\right)} \cdot \sin \left(\angle C\right) \approx 31.58611706$