I need help :'(

Find the sum of alldistinct of BC.

Hello Guest!

$c^2=a^2+b^2-2bc\ cos\ \gamma\\ 4^2=x^2+10^2-2\cdot 10\cdot x\cdot cos\frac{\pi}{6}\\ x^2-20\cdot cos\frac{\pi}{6}\cdot x+100-16\\ x=8.66\pm\sqrt{8.66^2-84}\\ x\in \{\}$

$BC\in\{\}$

  !

                  B

                          4

C 30°          10                  A

4^2  = 10^2 + BC^2  -  2 (10)(BC) ( sqrt 3)/2)

16 = 100 + BC^2  - (10sqrt 3)BC

BC^2 - (10sqrt 3)BC + 84   = 0

[ No real solutions for BC     since the discriminant is  negative ] 

Thanks for answering Asinus and CPhill!!!