Geometry 8-2 Trigonometric RatiosA 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 The sine (sin):

oppositesin

hypotenuse

2nd Trigonometric Ratio The cosine (cos):

adjacentcos

hypotenuse

3rd Trigonometric Ratio The tangent (tan):

oppositetan

adjacent

D

E F

12

5

13

Recall the 30°-60°-90° Special Right TriangleFind the sin of the 60° angle.

30°

2x

60°

3x

x

o

o

3sin(60 )

2

3sin(60 )

2

x

x

Recall the 45°-45°-90° Special Right TriangleFind the tan of the 45° angle.

o

o

tan(45 )

1tan(45 ) 1

1

x

x

45°

45°

x

x2x

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?

20°

4 x

osin(20 )4

sin(20)

1 44sin(20) 1.37

x

x

x

Find the length of side BC.

Another Example

o

o

10.2tan(15 )

tan(15 ) 10.2

1

x

x

tan(15) 10.2

10.238.07

tan(15)

x

x

10.2 ft

15°C B

A

ExampleFind the length of RT.

12°

TS

R

350 m

o 350cos(12 )

cos(12) 350

1cos(12) 350

350357.82

cos(12)

x

xx

x