Aptitude - Height and Distance

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"When ambition ends, happiness begins."

- (Proverb)

Trigonometry:

In a right angled OAB, where BOA = ,

i. sin = Perpendicular = AB ;

Hypotenuse OB

ii. cos = Base = OA ;

Hypotenuse OB

iii. tan = Perpendicular = AB ;

Base OA

iv. cosec = 1 = OB ;

sin AB

v. sec = 1 = OB ;

cos OA

vi. cot = 1 = OA ;

tan AB
Trigonometrical Identities:
1. sin² + cos² = 1.
2. 1 + tan² = sec² .
3. 1 + cot² = cosec² .

Values of T-ratios:

0� (/6)

30� (/4)

45� (/3)

60� (/2)

90�

sin 0

1

2

3

2

1

cos 1

3

2

1

2

0

tan 0

1

3

1 3 not defined

Angle of Elevation:

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the anlge of elevation of P as seen from O.

Angle of elevation of P from O = AOP.
Angle of Depression:

Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.