2 2 2 a b c 2 bc cos a 2 2 2 b a c 2 ac cos b
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Aug 06, 2023 •272 likes •338 views

Lesson 3.2: Law of Cosines 2 2 2 a b c 2 bc cos A 2 2 2 b a c 2 ac cos B 2 2 2 c a b 2 ab cos C Law of Cosines: Alternative Form 2 2 2 b c a cos A

  1. Lesson 3.2: Law of Cosines    2 2 2 a b c 2 bc cos A    2 2 2 b a c 2 ac cos B    2 2 2 c a b 2 ab cos C

  2. Law of Cosines: Alternative Form   2 2 2 b c a  cos A 2 bc   2 2 2 a c b  cos B 2 ac   2 2 2 a b c  cos C 2 ab

  3. Ex 1: Find all three angles of the triangle. m  A = 22 ° B m  B = 117 ° c = 14 a = 8 m  C = 41 ° A C b = 19   2 2 2     a b c 2 2 2 2 2 2 b c a a c b    cos C cos A cos B 2 ab 2 bc 2 ac

  4. Ex 2: Find the remaining angles and side of the triangle. 41 ° m  B = C a m  C = 24 ° b = 15 a = 21 115 ° B A c = 10   2 2 2 a c b     2 2 2 a b c 2 bc cos A cos B 2 ac    2 2 2 b a c 2 ac cos B   2 2 2 a b c  cos C    2 2 2 c a b 2 ab cos C 2 ab

  5. Heron’s Area Formula • Given any triangle with sides of lengths a, b, and c, the area of the triangle is:     ( )( )( ) Area s s a s b s c    where s ( a b c ) / 2

  6. Ex 3: Find the area of a triangular region having sides of lengths a = 43m, b = 53m, and c = 72m. b gb gb g b gb gb g     A     A s s a s b s c 84 84 43 84 53 84 72 b gb gb g s    ( 43 53 72 ) / 2  84 41 31 12  168 2 /  1281168 , ,  84  11319 2 . m Homework: p.291 #1-15 & 23-27 (all odds)

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