find the value of x.\n\nx =

Explanation:

Step1: Identify the trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In the right - triangle, $\theta = 60^{\circ}$, the opposite side to the $60^{\circ}$ angle is 7 and the adjacent side is $x$. So, $\tan60^{\circ}=\frac{7}{x}$.

Step2: Recall the value of $\tan60^{\circ}$

We know that $\tan60^{\circ}=\sqrt{3}$. So the equation becomes $\sqrt{3}=\frac{7}{x}$.

Step3: Solve for $x$

Cross - multiply to get $x\sqrt{3}=7$. Then $x = \frac{7}{\sqrt{3}}$. Rationalize the denominator: $x=\frac{7\sqrt{3}}{3}$.

Answer:

$\frac{7\sqrt{3}}{3}$