Question

If sin theta=a/b, then find the value of tan theta.

Answer 1

As sin theta is equal to Perpendicular/hypotenuse and tan theta is equal to perpendicular/base....and sin theta is given tan theta can be taken out by a Triangle method...

Answer 2

Given,

• Sinθ = a/b

To find,

• We have to find the value of tanθ.

Solution,

We can simply find the value of tanθ by using the concept of trigonometry.

As we know that Sinθ = Perpendicular/ Hypotenuse

and It is given that Sinθ = a/b = P/H

This implies Perpendicular = a, Hypotenuse = b

We know that Tanθ = perpendicular/base

we have to find the base first,

By using Pythagoras's theorem

         (H)² = (B)² + (P)²

          b²   = (B)² + a²

     b² - a² = (B)²

    $\sqrt{b^2-a^2}$ = B

Now, tan θ = P/B = a/$\sqrt{b^2-a^2}$

Hence, if sin theta=a/b, then the value of tan theta is a/$\sqrt{b^2-a^2}$.