1. Law of Sines We use law of Sines to find the length of a missing side or degree of a missing angle in an Oblique triangle(No Right Angle) In order to do this we must have some information and there are 4 conditions that will work, however only 2 use the law of Sines, so we will focus on those today. In order to use law of Sines you must know: 1.) 2 angles and 1 side ASA or 2.) 2 sides and an angle not between them(not included) SSA A B C a bc The three angles are A, B, and C with the side opposite the angles being a, b, and c.

2. Law of Sines In order to use law of Sines you must know: 1.) 2 angles and 1 side or 2.) 2 sides and an angle not between them(not included) A B C a bc The three angles are A, B, and C with the side opposite the angles being a, b, and c. Using Logic for rule 1: as long as we know two of the three angles A, B, or C and one side a, b, or c we can find both the other sides and the other angle. Using Logic for rule 2: if we know sides a and b then we need to know an angle other then C. If we know sides a and c then we need to know an angle other then B. If we know sides b and c then we need to know an angle other then A.

3. Law of Sines A B C a bc The three angles are A, B, and C with the side opposite the angles being a, b, and c. There is one last rule we need to recall from Geometry before we can start plugging away at these problems. The sum of the 3 angles of a triangle add to = ? Do you remember? 180 0 or

4. Lets look at some problems: A B C a b C = 20 105 0 40 0 Step 1 find the third angle using the sum of the angles of a triangle. A = 180 – 105 – 40 = 35 0 Step 2 Since we know C and c and all the angles we will use c/Sin C = (pick which one you want to find first)

5. Lets look at some problems: A B C a b c = 3 110 0 You Try Find: B, b, a 30 0

6. What if you are given 2 sides and and an angle. Ex. A = 60 0 a = 9 c = 10 Always draw a diagram first, and fill in the given information A B C a = 9 b C = 10 60 0 In this situation we use the law of Sines reciprocal (flipped) We always use the Angle and side we know both of. B = 180 – 60 – 74.21 = 45.79 0 Use the original form of law of Sines b = 7.45, B = 45.79 0, C = 74.21 0

7. You Try Use the law of Sines to solve the triangle round your answers to 2 decimal places. B = 100 0, c = 3, b = 5

8. Assignment #17 Pg.527 (17-31 odd)