```Chapter 9
Right Triangles and Trigonometry
Section 9.5
Sine, Cosine, Tangent
Definitions
sideoppsite ratio
A
a
A
trigonometric
side lengths
Sin A 
 is the ratio of the
sideoppsite
A of a
hypotenuse
Tan A 
two sides
of a right triangle
c

A  b
The
three
basic
trigonometric
ratios are Sine, Cosine,
Cos A 
c
and tangent
hypotenuse
B
Side
opposite a
A
C
c hypotenuse
b
to A
A
Find sin L, cos L, tan L, sin N, cos N, and tan N.
Express each ratio as a fraction and as a decimal.
Find sin A, cos A, tan A, sin B, cos B, and tan B.
Express each ratio as a fraction.
Use a calculator to find tan
thousandth.
KEYSTROKES: TAN
56
to the nearest ten
ENTER
1.482560969
Use a calculator to find cos
thousandth.
KEYSTROKES: COS
90
to the nearest ten
ENTER
0
a. Use a calculator to find sin 48° to the nearest ten
thousandth.
b. Use a calculator to find cos 85° to the nearest ten
thousandth.
EXERCISING A fitness trainer sets the incline on a
The walking surface is 5 feet long.
Approximately how many inches did the trainer raise
the end of the treadmill from the floor?
Let y be the height of the treadmill from the floor in inches.
The length of the treadmill is 5 feet, or 60 inches.
Multiply each side by 60.
Use a calculator to find y.
KEYSTROKES: 60
SIN
7
ENTER
7.312160604
CONSTRUCTION The bottom of a handicap ramp is
15 feet from the entrance of a building. If the angle of
how high does the ramp rise
off the ground to the nearest inch?
Find the value of each variable
sideoppsite A
Sin A 
hypotenuse
x
sin 36 
10
x = 10sin 36
x  5.8779
Cos A 
hypotenuse
y
cos36 
10
y = 10cos 36
y  8.090
Find the value of each variable
sideoppsite A
Tan A 
x
tan 48 
8
x = 8tan 48
x  8.8849
Cos A 
hypotenuse
8
cos 48 
y
y(cos 48) = 8
8
y
cos 48
y  11.9558
Find the value of each variable
x = 8(cos 64)
y = 8(sin 64)
x  3.5070
x  7.1903
```