Assume that the connecting rod and the crank of an engine forms as two sides of the triangle. If the area included in the triangle is maximum when the crank is at $60^\circ$, then the ratio of length of connecting rod to the radius of the crank is
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When the area is maximized, the crank and connecting rod form a right angle ($90^\circ$). This creates a standard $30^\circ-60^\circ-90^\circ$ right triangle, where the ratio of the opposite side to the adjacent side is always $\sqrt{3} \approx 1.732$.