in the diagram below, tan θ = √3. what is the...

# Explanation: ## Step1: Recall the tangent formula The formula for tangent in a right - triangle on the unit circle is $\tan\theta=\frac{y}{x}$. Given the point $(\frac{1}{2},m)$ on the terminal side of the angle $\theta$, $x = \frac{1}{2}$ and $y=m$. So $\tan\theta=\frac{m}{\frac{1}{2}}$. ## Step2: Substitute the given value of tangent We know that $\tan\theta=\sqrt{3}$. Substituting into the equation $\tan\theta=\frac{m}{\frac{1}{2}}$, we get $\sqrt{3}=\frac{m}{\frac{1}{2}}$. ## Step3: Solve for $m$ To solve for $m$, we multiply both sides of the equation $\sqrt{3}=\frac{m}{\frac{1}{2}}$ by $\frac{1}{2}$. Using the rule $a=\frac{b}{c}\Rightarrow b = a\times c$, we have $m=\frac{1}{2}\times\sqrt{3}=\frac{\sqrt{3}}{2}$. # Answer: $\frac{\sqrt{3}}{2}$