# Aptitude :: Height and Distance

Exercise : Height and Distance - Formulas
1. 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

2. Trigonometrical Identities:

1. sin2 + cos2 = 1.

2. 1 + tan2 = sec2 .

3. 1 + cot2 = cosec2 .

3. Values of T-ratios:

(/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

4. 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 angle of elevation of P as seen from O.

Angle of elevation of P from O = AOP.

5. 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.