Basic Sine Rule Question Here’s a simple example of using the sine rule to find an angle and then the length of a side of a triangle. Attempt the question without help. If you get stuck, or think you have the final answer then you can work your way through the presentation. It has been designed to allow you to view a fully worked solution line by line. Try to do as much as possible by yourself and only advance the lines when you’ve done everything you can. ADJ © 2005 L.A.P.D.

a b Consider the triangle below. Use the sine rule to find angle B and then line c = sin A sin B 43.6 30 = sin 120 sin B cross multiplying b = 30 m A=120 43.6 sin B = 30 sin 120 c = ? 43.6 sin B = 30( 3) /2 B=? 43.6 sin B = 25.98 a = 43.6 m sin B = 25.98 / 43.6 B = sin–1 (25.98 / 43.6) B = 36.6

To find line c we first find angle C. A + B + C = 180 This can be found by remembering that the sum of the angles in any triangle is 180 C = 180 - 120 - 36.6 C = 23.4 b = 30 m A=120 C=? c = ? B= 36.6 a = 43.6 m

a c Line c can then be found by the sine rule or the cosine rule. We’ll use the sine rule because that’s what we were asked to do. = sin A sin C 43.6 c = sin 120 sin 23.4  cross multiplying c sin 120 = 43.6 sin 23.4 b = 30 m C= 23.4 A=120 c c ( 3) /2 = 43.6 sin 23.4 B= 36.6 0.866 c = 43.6 x 0.397 a = 43.6 m 0.866 c = 17.3 c = 17.3 / 0.866 c = 20.0 m