Question

What is $tan\theta$ in $△$ABC, if $\theta$ is increased by ${30}^{\circ }$.

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. Not defined.

Answer 1

The correct option is C Not defined.

In $△ABC$, if $\theta$ is increased by ${30}^{\circ }$, $\theta ={60}^{\circ }+{30}^{\circ }={90}^{\circ }$.
As the value of $\theta$ increases, the length of side AC decreases and eventually, points A and C coincide.

Then the length of AC will be '0' units.

$\therefore tanA=\frac{BC}{AC}=\frac{BC}{0}$, which is not defined.

Or, we can say that when $\theta$ is increased by ${30}^{\circ }$, its value will be ${90}^{\circ }$.
And $tan{90}^{\circ }$ is not defined.