let c5 angle C120 degrees and angle b30 degrees Find the mea

let c=5, angle C=120 degrees, and angle b=30 degrees. Find the measure of angle A(in degrees) and the length of sides a and b. Give your anser to at least 3 decimal places.

Solution

c = 5

angle C = 120 deg

angle B = 30 degrees

therefore, by triangle rule sum of angles of a triangle = 180 degrees

angle A = 180 - ( 120 + 30) = 30 degrees

applying sine rule to find the length of a and b

c / sin C = b / sin B

5 / sin 120 = b / sin 30

b = 2.886

and

c / sin C = a / sin A

a = 2.886