# Given a scalene triangle with angles of A=38, B=83 and C=59, side opposite to angle C is measuring 20, how do you find lengths of other sides?

May 25, 2015

Assuming a triangle with sides $a , b , c$ opposite angles $A , B , C$ respectively
The Law of Sines says
$\frac{a}{\sin} \left(A\right) = \frac{b}{\sin} \left(B\right) = \frac{c}{\sin} \left(C\right)$

for the given values this becomes
$\frac{a}{\sin} \left({38}^{\circ}\right) = \frac{b}{\sin} \left({83}^{\circ}\right) = \frac{20}{\sin} \left({59}^{\circ}\right)$

$a = \frac{20}{\sin} \left({59}^{\circ}\right) \cdot \sin \left({38}^{\circ}\right) = 12.88136$

$b = \frac{20}{\sin} \left({59}^{\circ}\right) \cdot \sin \left({83}^{\circ}\right) = 28.13559$