Trigonometric Ratios - Mathematics and Statistics for the Environment - page 102

TABLE 6.1
Definition of Trigonometric Ratios

Measureofleg opposite angle
Measureofh

A

sin Aac =

Sine of angle A

ypotenuse

Measureofleg adjacenttoangle
Measureo

A

cos Abc =

Cosine of angle A

f hypotenuse

Measureofleg opposite angle
Measureofl

A
eg adjacenttoangle A

tan Aab =

Tangent of angle A

B

c

a

A b C

FIGURE 6.1 Right triangle.

x

15

9

z y

12

FIGURE 6.2 Illustration for Examples 6.1 and 6.2.

■ EXAMPLE 6.1
Problem: Find the sine, cosine, and tangent of angle Y in Figure 6.2.

Solution:

Opposite leg
Hypotenuse

9
15

sin Y = = = 060 .

Ad jacentleg

Hypotenuse

12
15

cos Y = == 080 .

Opposit eeleg

Adjacentleg

9
12

tan Y = == 075 .