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

A = 79.1°, B = 29.9°, b = 49.3; A = 100.9°, B = 8.1°, b = 49.3

A = 10.9°, B = 98.1°, b = 24.8; A = 169.1°, B = 81.9°, b = 24.8

A = 79.1°, B = 29.9°, b = 13.7; A = 100.9°, B = 8.1°, b = 3.9

A = 10.9°, B = 98.1°, b = 27.2; A = 169.1°, B = 81.9°, b = 27.2

Answer 1

This is really kind of a confusing one. See when you do the triangle with the info given you come up with this for a drawing:

Answer 2

hmmm

Answer 3

If angle A equals 79 degrees, it has a sin of .9816271834 BUT when you subtract 79 from 180 you get 101 and the sin(101) is also .9816271834 So there are two angles that satisfy angle A...79 and 101.

Answer 4

So let's draw these two triangles out using the angles of 79.1 and 100.9 (which are the actual measurements with a decimal. I rounded up in the explanation.)

Answer 5

now we need to find side b using the law of sines as well.