Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. C = 71°, a = 27, c = 26

Answer 1

We have

SinC/ c = Sin A / a

Sin 71/ 26 = Sin A / 27

Sin A = 27 Sin 71 / 26 = about .982

So°

Sin-1(.982) = A = 79. 08°

Then angle B = 180 - 71 - 79.08 = 29.92°

And b is given by

b/sin29.92 = 26/sin 71

b = 26sin29.92/sin71 = about 13.72

But A could also be an obtuse angle = 180 - 79.08 = 100.92°

So we have

B = 180 - 71 - 100.92 = 8.08°

And we have

b / sin 8.08 = 26/sin71

b = 26sin8.08/sin 71 = 3.865