Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

7.2 Measurement of Length 167

In theright triangleshown, the angle facing sideais denoted by a(alpha), and the angle

facing sidebby b(beta). The sine, cosine, and the tangent of an angle are defined by

The sine and the cosine law (rule) for anarbitrarily shaped triangleis

or

cos u

a

2

b

2

c

2

2 ba

cos b

a

2

c

2

b

2

2 ac

cos a

b

2

c

2

a

2

2 bc

c

2

a

2

b

2

 2 ba 1 cos u 2

b

2

a

2

c

2

 2 ac 1 cos b 2

The cosine rule: a

2

b

2

c

2

 2 bc 1 cos a 2

The sine rule:

a

sin a



b

sin b



c

sin u

tan b

sin b

cos b



opposite

adjacent



b

a

cos b

adjacent

hypotenuse



a

c

sin b

opposite

hypotenuse



b

c

tan a

sin a

cos a



opposite

adjacent



a

b

cos a

adjacent

hypotenuse



b

c

sin a

opposite

hypotenuse



a

c

H

h 2

h 1



d

tan  =

h 2

d

H = h 1  h 2 = h 1  d tan 

90

80100

10080

11070

12060

13050

14040

15030

16020

17010

701106012050

1301404030

15020

16010

170

Straw

Protractor

String

Mass



■Figure 7.3

Measuring the height of a building

indirectly.

90

Hypotenuse

b

a

c





b

a

c







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