Question

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Explanation:

Step1: Recall cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 60^{\circ}$, the adjacent side is $x$, and the hypotenuse is $52\sqrt{30}$.

Step2: Substitute values into formula

We know that $\cos60^{\circ}=\frac{1}{2}$. So, $\frac{x}{52\sqrt{30}}=\frac{1}{2}$.

Step3: Solve for $x$

Cross - multiply: $x=\frac{1}{2}\times52\sqrt{30}$. Simplify: $x = 26\sqrt{30}$.

Answer:

$26\sqrt{30}$