Height and Distance - Important Formulas |Aptitude

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:

   	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

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.