Steven W. answered • 07/06/16

College Instructor in Algebra and Trigonometry

The law of sines for a triangle, in one form, is that:

(sin A)/a = (sin B)/b = (sin C)/c, where a, b, and c are the side lengths and A, B, and C are the corresponding angles opposite those sides.

2) and 3) can be solved directly with this. For example, for 2)

(sin 135)/45 = (sin 10)/b

Cross-multiplying gives: b(sin 135) = 45(sin 10) --> b = 45((sin 10)/sin(135)) ~ 45(0.246) = 11.05

3) can be solved in exactly the same way, just using (sin A)/a in place of (sin C)/c

For 1), we have to do a little extra work, because B is not given. But, for a triangle, the sum pf interior angles must equal 180 degrees. So 24.3 + 54.6 + B = 180, and B = 180 - 24.3 - 54.6 = 101.1 degrees. Then, just follow the same procedure as above.

Hope this helps!

Hannah L.

07/06/16