Consider a triangle ABC like the one below Suppose that a 55

Consider a triangle ABC like the one below. Suppose that a= 55, c= 64, and A =27 degree. (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 no such triangle exists, enter \"No solution.\" If there is more than one solution, use the \"or\" button.

Solution

A=27,a=55 c=64

We use sine law here which is

Sin A/a= Sin C/c

sin 27/ 55= sin C/64

sin C= 64 sin 27/55

C= sin^-1(64sin27/55)

C=31.8893degree

B= 180-(A+C)

B= 180-(27+31.8893)

B=121.1107 degree

Sin B/b= SinA/a

Sin 121.1107/b=sin 27/55

b= 55 sin 121.1107/sin 27

b= 103.7233