Question

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Explanation:

Step1: Use sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, for the $60^{\circ}$ angle, $\sin60^{\circ}=\frac{5}{x}$.
Since $\sin60^{\circ}=\frac{\sqrt{3}}{2}$, we have the equation $\frac{\sqrt{3}}{2}=\frac{5}{x}$.

Step2: Solve for $x$

Cross - multiply the equation $\frac{\sqrt{3}}{2}=\frac{5}{x}$ to get $\sqrt{3}x = 10$.
Then $x=\frac{10}{\sqrt{3}}$.
Rationalize the denominator: $x=\frac{10\sqrt{3}}{3}$.

Answer:

$x = \frac{10\sqrt{3}}{3}$