Law of Cosines C a b A B c.

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Presentation transcript:

Law of Cosines C a b A B c

: -1≤ cosØ ≤1 when 0˚≤ Ø ≤180˚ : To use the Law of Cosines, you must know 3 things, one of which is a side. : If you know an angle, start by finding its corresponding side. : Using the Law of Cosines will result in only 1 solution because there is only 1 angle between 0˚ and 180˚ with the given cosine.

: We find C by taking 180-(sum of A+B). Ex: Solve each triangle. Round angle measures to the nearest minute & side measures to the nearest tenth. 1. a=1.5, b=2.3, c=1.9 Since we know all 3 sides, we can pick any side to start with: Now we can use either Law of Sines or Law of Cosines. Recall that Law of Sines may result in more than 1 answer. A= a=1.5 B= b=2.3 C= c=1.9 40˚28’ : We find C by taking 180-(sum of A+B). 84˚16’ 55˚16’

: We find C by taking 180-(sum of A+B). Ex: Solve each triangle. Round angle measures to the nearest minute & side measures to the nearest tenth. 2. b=40, c=45, A=51˚ Since we know 2 sides and angle A, find a: Now we can use either Law of Sines or Law of Cosines. Recall that Law of Sines may result in more than 1 answer. A= 51˚ a= B= b=40 C= c=45 36.9 : We find C by taking 180-(sum of A+B). 57˚27’ 71˚33’