Question

5.If 3 tan A=4, then find sin A and cos​

Answer 1

Step-by-step explanation:

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

Answer 2

Let ABC is a right angle triangle

3tanA=4 ⇒tanA=$\dfrac{4}{3}$=$\dfrac{BC}{AB}$ .

by using Pythagoras theorem

AC²=AB²+BC²

=(3)²+(4)²

=9+16=25

∴AC=√25=5

sinA=$\dfrac{Opposite side of∠A}{Hypotenuse}$

=$\dfrac{BC}{AC}$= $\dfrac{4}{5}$

∴cosA=$\dfrac{Adjacent side of∠A}{Hypotenuse}$

=$\dfrac{AB}{AC}$ =$\dfrac{3}{5}$

∴sinA= $\dfrac{4}{5}$ and cosA= $\dfrac{3}{5}$