Transcript Chapter 5/6 Review Trigonometry

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