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Question

In a right ABC, if A is acute and tanA = 3/4, find the remaining trigonometric ratios of A.

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Solution

Consider a Δ 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, SinA = opposite/Hypotenuse

SinA = 3/5

Similarly , CosA = 4/5

Hence , CosecA = 5/3 ; SecA = 5/4 ; CotA = 4/3


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