Question

In the given figure, if the value of $\sin \theta$ is $\frac{a}{b}$, find the value of $tan\theta$.

• A. $\frac{b}{a}$
• B. $\frac{a+b}{b}$
• C. $\frac{a}{\sqrt{b^2-a^2}}$
• D. $\frac{b}{\sqrt{b^2-a^2}}$

Answer 1

The correct option is C $\frac{a}{\sqrt{b^2-a^2}}$

Since $\sin \theta$=$\frac{Oppositeside}{Hypotenuse}$,

Opposite side = $a$
Hypotenuse = $b$

Since this is a right angled triangle, we can apply the Pythagoras theorem to find the adjacent side.

According to Pythagoras Theorem,
Adjacent side=$\sqrt{b^2-a^2}$

Since $\tan \theta$=$\frac{Oppositeside}{Adjacentside}$

The value of $\tan \theta$ is $\frac{a}{\sqrt{b^2-a^2}}$