6 2 Law of Cosines fguilbert In any

6. 2 Law of Cosines fguilbert

In any triangle, the Law of Cosines says: 2 c = 2 a + 2 b - 2 ab Cos C C A fguilbert B

Side a is opposite < A. A Side b is opposite < B Sice c is opposite < C 2 2 2 c = a + b - 2 ab Cos C C b a c A B fguilbert

When is the Law of Cos used? b A C c fguilbert a B

CASE 1 Two sides and the included angle are known (SAS). CASE 2: Three sides are known (SSS). fguilbert

The basic form of the Law of Cosines is : 2 c = 2 a + 2 b - 2 ab Cos C but other letters are changed Although this is < C, you can use the formula for A or B fguilbert

C A fguilbert

3 A C a A B 4 fguilbert

C 3 A a 4 fguilbert B

C 3 A a 4 B Be careful not to combine these. Order of op. 2 0 a = 9 + 16 - 24 cos 40 2 a = 25 - 24 cos fguilbert 0 40

C 3 A 40 a 4 fguilbert B

Find <A 2 c 2 a A 29 17 B 35 2 b C = + - 2 ab Cos C 2 2 2 a = b + c - 2 bc Cos A 2 2 2 35 =29 +17 - 2(29)(17)c fguilbert

Find <A A 29 17 B 35 2 2 2 35 =29 +17 - 2(29)(17)c 1225= 1130 - 986 cos. A -1130 95 = - 986 cos. A fguilbert C

Find <A A 17 B 35 95 = 986 cos. A ___ -986 29 -986 -. 0963 = cos A 0 95. 5 = A fguilbert C

Find <A A 29 17 B 35 C To find B or C now, it would b quicker to use the Sine Law. Both B and C must be acute. fguilbert

How to Choose the right one. SAS SSS ASA SSA Law COS Law SINES (0, 1, 2 triangles are possible) fguilbert

thought for the day One who lacks the courage to start, is already finished. fguilbert