Solve the triangle using the law of sines Assume b 8 A 30

Solve the triangle using the law of sines.  (Assume b = 8, A = 30°, and C = 110°. Round the lengths to two decimal places, and the angle to the nearest degree.)

Solution

b = 8

angle A = 30

angle C = 110

angle B = 180 - ( 110 + 30) = 40 degrees

since sum of 3 angles of a triangle = 180 degrees

applying sine rule

b / sin B = a / sin A

plugging the values

8 / sin 40 = a / sin 30

a = ( 8 / sin 40 )* sin 30 = 6.22

similarly

c = ( 8 / sin 40 ) * sin 110 = 11.70