Download Geometry 8-2 Trig Ratios

Geometry 8-2
Trigonometric Ratios
A trigonometric (trig) ratio is a ratio of two
sides of a right triangle.
Use trig ratios when the right triangle only
has one side length given and it is not a
special right triangle (30-60 or 45-45)
1st Trigonometric Ratio
opposite
 The sine (sin):
sin 
hypotenuse
2nd Trigonometric Ratio
adjacent
 The cosine (cos): cos 
hypotenuse
3rd Trigonometric Ratio
opposite
 The tangent (tan): tan 
adjacent
D
13
12
E
5
F
Recall the 30°-60°-90°
Special Right Triangle
Find the sin of the 60° angle.
60°
2x
x
30°
x 3
x 3
sin(60 ) 
2x
3
o
sin(60 ) 
2
o
Recall the 45°-45°-90°
Special Right Triangle
Find the tan of the 45° angle.
45°
x 2
45°
x
x
x
tan(45 ) 
x
1
o
tan(45 )   1
1
o
Word Problem
 You
and your friends decide to build a
bike ramp using a 4 ft piece of wood.
You make a 20° angle with the ground.
How high above the ground will the back
wheel be when your bike goes off the
ramp?
x
sin(20o ) 
4
20°
x
4
sin(20) x

1
4
x  4sin(20)  1.37
Another Example
 Find
the length of side BC.
A
10.2 ft
C
10.2
tan(15 ) 
x
tan(15o ) 10.2

1
x
o
15°
B
x tan(15)  10.2
10.2
x
 38.07
tan(15)
Example
Find the length of RT.
R
12°
350 m
S
T
350
cos(12 ) 
x
cos(12) 350

1
x
x cos(12)  350
350
x
 357.82
cos(12)
o