If sin A = 1/3 find the value of tan A

We have,

sin A = 1/3 ……..….. (1)

As we know, by sin definition;

sin A = Perpendicular/ Hypotenuse = 1/3 ….(2)

By comparing eq. (1) and (2), we have

Opposite side = 1 and Hypotenuse = 3

Now, on using Pythagoras theorem in Δ ABC

Hypotenuse2= Base2 + Perpendicular²

⇒ 3² = Base² + 12

Base 2= 3² – 1²

= 9 – 1

= 8

Base = √8 = 2√2

Hence, Base = 2√2

By definition,

cos A = Base/Hypotenuse

⇒ cos A = 2√2/3

tan A = Perpendicular/Base

⇒ tan A = 1/2√2

Answer

tan A = 1/2√2