Download 10.4 - 10.5 Trigonometric Ratios (SOH-CAH-TOA)

Chapter 10: Right Triangle Trigonometry
10.4 - 10.5 Trigonometric Ratios
(SOH-CAH-TOA)
Trigonometry - a branch of mathematics that studies
the relationships between the sides and angles of
triangles.
Trigonometric ratio - the ratio between two sides of a
right triangle.
There are 3 "trig ratios" that we will study.
The ratios are called sine, cosine, and tangent.
They are abbreviated sin, cos, and tan respectively
(locate these buttons on your calculator).
A
c
b
C
a
B
What do these trig ratios stand for?
adjacent side
opposite side
sin x =
hypotenuse
cos x = hypotenuse
CAH
SOH
opposite side
tan x = adjacent side
TOA
The mnemonic device to remember the 3 trig ratios is
"SOH-CAH-TOA"
SOHCAHTOA
A
5
3
C
4
B
Example 1: Let's look at <A.
Find the side opposite, side adjacent, and the
hypotenuse for <A.
Then write the sin A, cos A, and tan A ratios.
Example 2
D
6
E
Find sin F, cos F, and tan F.
10
8
F
L
J
What is the side opposite of <J?
What is the hypotenuse of the triangle?
What is the side adjacent to <J?
What is sin R?
K
Q
13
What is cos R?
What is tan R?
7
R
9
S
Using Trigonometric Ratios to find side lengths
(You will need a calculator for this)
Solve for the missing side lengths:
G
25
E
o
B
o
40
x
12
16
x
D
E
M
K
C
70
o
11
10
E
y
A
J
58
o
x
L
Solve for the missing side lengths:
P
o
22
y
L
9
x
M
How do we solve if the variable is in the denominator
of the fraction?
K
B
x
x
41o
19
23
48o
J
L
A
C
A
K
27o
x
x
15
o
J
7
L
L
64
B
Using Inverse Trigonometric Ratios to
find angle measures
(You will need a calculator for this)
In this section you will need to use the inverse trig
functions to solve for missing angles. Just as the
following are inverses and undo each other,
Addition inverse Subtraction
Multiplication inverse Division
Square inverse Square Root
so does a trig ratio and its inverse.
sinθ inverse sin-1θ
cosθ
inverse
inverse
tanθ
cos-1θ
tan-1θ
"To find the degree, use the inverse key"
Solve for the missing angle measures:
5
D
E
R
y
24
8
7
x
Q
y
S
x
C
P
A
9
B
x
x
12
15
y
y
C
E
18
N