# If Sin A = $$3\over 4$$, Calculate Cos A and Tan A.

## Solution :

Consider a triangle ABC in which $$\angle$$ B = 90

For $$\angle$$ A, we have :

Base = AB, Perpendicular = BC and Hypotenuse = AC,

$$\therefore$$  Sin A = $$perpendicular\over hypotenuse$$ = $$BC\over AC$$ = $$3\over 4$$

Let BC = 3k and AC = 4k,

Then,  $${AB}^2$$ = $${AC}^2 – {BC}^2$$ = $$\sqrt{7}$$

$$\therefore$$  cos A = $$Base\over Hypotenuse$$ = $$AB\over AC$$ = $$\sqrt{7}\over 4$$

and  tan A = $$perpendicular\over hypotenuse$$ = $$BC\over AB$$ = $$3\over \sqrt{7}$$