A Sangaku-like Puzzle from Japan
<p>Consider the right-angled triangle on the bottom right. The opposite side is 1 as it’s the unit length of the square.</p>
<p>Using the tangent function, we find the length of the adjacent side of the triangle. </p>
<p>Therefore, we can sum up the three segments to find the side length of the equilateral triangle.</p>
<p>So how do we show that the area of the outer triangle is about twenty times that of the inner triangle? Notice that <strong>the inner triangle is in fact an equilateral triangle with side length 1</strong>.</p>
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