Question

If 3 tan A = 4 , then find Sin A and Cos A.​​

Answer 1

3tanA = 4

tanA = 4/3

tanA = opp/adj = 4/3

hyp² =s²+s²

h² = 16 +9

h² = 25

h = 5

sin A = opp / hyp

= 4/5

cos A = adj/hyp

= 3/5

∴sin A = 4/5

cos A = 3/5

Answer 2

Answer:

Let ABC is a right angle triangle

3tanA=4 ⇒tanA=

3

4

=

AB

BC

By using Pythagoras theorem

AC

2

=AB

2

+BC

2

=(3)

2

+(4)

2

=9+16=25

∴AC=

25

=5

sinA=

Hypotenuse

Opposite side of∠A

=

AC

BC

=

5

4

∴cosA=

Hypotenuse

Adjacent side of∠A

=

AC

AB

=

5

3

∴sinA=

5

4

and cosA=

5

4

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