A person standing on the top of a cliff $150$ m high observes two boats in a straight line with the base of the cliff. The angles of depression of the two boats are $45^\circ$ and $60^\circ$. Find the distance between the boats if they are on the same side of the cliff.

Options:

• A: $50(3 + \sqrt{3})$ m
• B: $50(3 - \sqrt{3})$ m
• C: $150(\sqrt{3} - 1)$ m
• D: $150(3 - \sqrt{3})$ m

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