1. The Sine Law How to use sine law to find the angles and lengths of triangles.

2. ab A c B C = Sin ASin B ab The basics of Sine Law

3. 5.9m (a) 7.8m (b) c B C A = Sin ASin B ab = Sin 36˚Sin B 5.97.8 36 ˚ =SinB x 5.9(Sin36˚)(7.8) =SinB(Sin36˚)(7.8) 5.9 =<B(Sin36˚)(7.8) 5.9 Sinˉ¹ Solve with Calculator The whole point is to find the two missing angles and side. EX 1

4. =<B51 ˚ Now to find angle C <A + <B + <C = 180˚ <C = 180˚ - (51˚ + 36˚) 51˚ + 36˚ + <C = 180˚ <C = 93 = Sin ASin C ac = Sin36˚Sin93˚ 5.9c = Sin36˚ 5.9 cSin93˚ x 10.0m = c

5. EX 2 θ θ E C B A 15.6m 36.0m = Sin BSin C bc = Sin θSin140˚ 15.636.0 Θ= sinˉ¹ (15.6)(sin140˚) 36.0 N Θ=16˚ <NAC= 90˚ -16˚ <NAC= 74˚ We want to find angle NAC

6. Try this one out 115˚ 16m 49m A C B C

7. = Sin ASin115˚ 1649 A= Sinˉ¹ (sin115˚)(16) 49 A= 31˚ C=180-(31+115) C= 180 - 146 C=34˚ = Sin ASin C ac = Sin31˚Sin34˚ 16c = Sin31˚ 16 cSin34˚ x -20.95 = c