Consider a triangle ABC like the one below Suppose that C 1

Consider a triangle ABC like the one below. Suppose that C = 115degree, a = 55, and b = 33. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled \"or\".

Solution

by law of cosines

c=[a²+b²-2abcosC]

c=[55²+33²-2*55*33*cos115^o]

c=75.2

by law of sines

a/sinA=b/sinB=c/sinC

a/sinA=c/sinC

55/sinA=75.2/sin115

sinA=55*sin115/75.2

A=41.5^o

b/sinB=c/sinC

33/sinB=75.2/sin115

sinB=33*sin115 /75.2

B=23.5^o