Finding sin, cos, tan when sides of a triangle are given

In Δ ABC, right angled at B. AB = 12 cm, BC = 5cm.

Find sin A, cos A, tan A, cosec A, sec A, cot A

First we draw the triangle

Step 1 : Finding sides of triangle

In right triangle ABC,

Using Pythagoras theorem

(Hypotenuse) ²  = (Height) ²  + (Base) ²

AC ²   = AB ²  + BC ²

AC ²  = 122 + 52

AC ²  = 144 + 25

AC ²   = 169

AC = √169

AC = √(13 ×13) =√(13 ² ) = 13

Hence AC = 13 cm

So, our triangle becomes

Step 2 : Finding sin A , cos A, tan A

Now, let us find cosec, cot and tan