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2 2 2 a b c 2 bc cos a 2 2 2 b a c 2 ac cos b

Aug 06, 2023 272 likes •343 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

SLIDE 1

Lesson 3.2: Law of Cosines

a b c bc A b a c ac B c a b ab C

2 2 2 2 2 2 2 2 2

2 2 2          cos cos cos

SLIDE 2

cos cos cos A b c a bc B a c b ac C a b c ab         

2 2 2 2 2 2 2 2 2

2 2 2

Law of Cosines: Alternative Form

SLIDE 3

Ex 1: Find all three angles of the triangle.

a = 8 c = 14 b = 19 C B A

mA = mB = mC =

cos A b c a bc   

2 2 2

cosB a c b ac   

2 2 2

cosC a b c ab   

2 2 2

22° 117° 41°

SLIDE 4

Ex 2: Find the remaining angles and side of the triangle.

C B A a b = 15 c = 10

mB = mC = a =

115°

a b c bc A b a c ac B c a b ab C

2 2 2 2 2 2 2 2 2

2 2 2          cos cos cos

cosB a c b ac   

2 2 2

cosC a b c ab   

2 2 2

41° 24°

SLIDE 5

Heron’s Area Formula

Given any triangle with sides of

lengths a, b, and c, the area of the triangle is:

2 / ) ( ) )( )( ( c b a s where c s b s a s s Area       

SLIDE 6

Ex 3: Find the area of a triangular region having sides of lengths a = 43m, b = 53m, and c = 72m.

Homework: p.291 #1-15 & 23-27 (all odds)

s    ( ) / 43 53 72 2 A s s a s b s c    

b gb gb g

168 2 /  84

A     84 84 43 84 53 84 72

b gb gb g

 84 41 31 12

b gb gb g

 1281168 , , 11319

. m