Consider a triangle ABC like the one below Suppose that a 2

Consider a triangle ABC like the one below. Suppose that a = 27, h 46, and c - 67. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to .it least four decimal places, and round your answers to the nearest If there is more than one solution, use the button labeled \'or\'.

Solution

a = 27

b = 46

c = 67

applying cosine rule

c^2 = a^2 + b^2 - 2ab cos C

plugging the values

67^2 = 27^2 + 46^2 - 2(27)(46) cos C

4489 = 2845 - 2484 cos C

cos C = 1644 / - 2484

C = 131.43 degrees

applying sine rule

c / sin C = b / sin B

67 / sin 131.43 = 46 / sin B

sin B = 46 / 89.36

B = 39.98 degrees

sin A = 27 / 89.36

A = 17.58 degrees