In a right △ABC, if ∠ A is acute and tanA = 3/4, find the remaining trigonometric ratios of ∠ A.
Consider a △ ABC in which ∠B = 90∘
For ∠A , we have :
Base = AB, perpendicular = BC and hypotenuse = AC
∴ tan A = PerpendicularBase = 34
⇒ BCAB=34
Let, BC = 3x units and AB = 4x units.
Then, AC = √AB2+BC2
= √(4x)2+(3x)2
= √(25x2) = 5x units.
Now, sin A = 35 and cos A = 45