With respect to ∠A, the ratios of trigonometry are given as:

• sine: Sine of an angle is defined as the ratio of the side opposite(perpendicular side) to that angle to the hypotenuse.
• cosine: Cosine of an angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.
• tangent: Tangent of an angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.

• It will help if you have a way of recalling these definitions. One of these ways is by remembering
  
  SOH TOA CAH

sine is opposite over hypotenuse,
tangent is opposite over adjacent
and cosine is adjacent over hypotenuse.
Some people remember it as

simply changing the syllables around.
Others remember it by a little verse:
Tom’s Old Aunt (TOA)
Sat On Him (SOH)
Cursing At Him. (CAH)
Whichever you learn, it will be helpful in order to remember these ratios.

EXAMPLE

The base of the right-angled triangle shown is 5 cm in length,  and the angle A is 60°.
(I) Calculate cosine of ∠BAC.

(II)Calculate the value of h.

SOLUTION

(I) SINCE IN RELATION TO ANGLE 60^O SIDE AC IS ADJACENT AND SIDE AB IS THE HYPOTENUSE, THEREFORE THE TRIGONOMETRIC RATIO THAT WILL BE USED IS COSINE.

SINCE  COSINE = ADJACENT/HYPOTENUSE

THEN COS60^O = 5/10 = 0.5

(II) USING PYTHOGRAS THEOREM,

h = √(10² - 5²)

    =8.6603

Given the right triangle below, find 
sin A, cos A and tan A