Question

in the diagram below, tan θ = √3. what is the value of m?

Explanation:

Step1: Recall the tangent - definition

The formula for the tangent of an angle $\theta$ in a right - triangle formed in the unit circle is $\tan\theta=\frac{y}{x}$, where $(x,y)$ is a point on the terminal side of the angle $\theta$. Given $x = \frac{1}{2}$ and $\tan\theta=\sqrt{3}$, and $\tan\theta=\frac{m}{\frac{1}{2}}$.

Step2: Solve for $m$

Since $\tan\theta=\frac{m}{\frac{1}{2}}=\sqrt{3}$, we can cross - multiply. We get $m=\sqrt{3}\times\frac{1}{2}=\frac{\sqrt{3}}{2}$.

Answer:

$\frac{\sqrt{3}}{2}$