How do you find perimeter of a triangle with 1 side given the angles are 105, 45, and 30 and the only side given is 8, opposite of the angle 30?

Perimeter: ##34.76852## (to the limit of my calculator)

Let ##a## be the length of the side opposite the ##45^@## angle and ##b## the length of the side opposite the ##105^@## angle.

tells us ##color(white)("XXX")8/sin(30^@)=a/sin(45^@)=b/sin(105^@)##

##sin(30^@)=0.5## ##sin(45^@)=0.707107## (approx.) ##sin(105^@)=0.965926## (approx.)

##8/sin(30^@)=16##

##a=16xxsin(45^@)=11.31371##

##b=16xxsin(105^@)=15.45481##

##"Perimeter" = 8 + a + b##

##color(white)("XXXXX")=34.76852##