Right Angle Trigonometry sin A opp hyp cos A Opposite Hypotenuses adj hyp tan A opp A Adjacent adj These relationships can only be used with a 90o angle. SOH CAH TOA can be used to help remember the ratios Example 1: Calculating a Side sin 40 5 x 1 sin 40 x 5 Decide which angle and which 2 sides to use x 5 1 sin 40 In this case angle = 40, opp = 5, hyp = x x 7 . 78 opp and hyp is sin flip the fractions to get x in the top cross multiply Example 2: Calculating an Angle Decide which angle and which 2 sides to use In this case angle = A, adj = 5, hyp = 7 adj and hyp is cos use cos-1 to calculate an angle Non-Right Angle Trigonometry SIN LAW sin A a sin B b sin C c a OR sin A b sin B c sin C Side a is opposite angle A, side B opposite angle b, etc To use sin law, you must know one side-angle pair and you must also know one other side. Examples : Sin Law sin B sin 35 7 B sin 5 1 7 sin 35 5 B 52 . 42 COS LAW a b c 2 ( b )( c )(cos A ) 2 2 2 b a c 2 ( a )( c )(cos B ) 2 2 2 c a b 2 ( a )( b )(cos C ) 2 2 2 Used when you do not have a side-angle pair Examples : Cos Law a 5 7 2 ( 5 )( 7 ) cos 35 6 5 4 2 ( 4 )( 5 ) cos B a 25 49 70 cos 35 36 25 16 40 cos B a 74 70 cos 35 40 cos B 5 a 16 . 659 ..... cos B 5 a B cos 2 2 2 2 2 2 16 . 659 ... a 4 . 08 2 2 2 1 40 5 40 B 82 . 82 o Chapter 5 – Primary Trig Ratios and Similar Triangles Find out if 2 triangles are congruent - Ch. review p.515, #1 Find out if 2 triangles are similar - Ch. review p.p.515, #2 & p.518#3-6 & p.538,#1-3 & p.586#1,2 Find missing sides or angles in a right angle triangle - Ch. review p.522,#1114 & Ch. review test p.526,#1abc,2-7 Chapter 6 – Trig for Non-Right Angle Triangles Find missing sides or angles in a non-right angle triangle Ch. review p.582,#4-6 & p.585,#10-12 & Ch. review test p.3-10 Find missing sides or angles in a non-right angle triangle Ch. review p.583,#7-9 & p.585,#10-12 & Ch. review test p.3-10