Two squares with areas of 1 and 3 are inscribed in a square frame. What’s the angle?

Scroll down for a solution to this problem.

## Solution

The angle is 30°.

From the areas we can infer the lengths as shown. It is also straightforward from comparing angles that the right triangles in the top are similar. Therefore we can say x/√3=1/(x+√3-1). This gives x=1, so in fact the triangles are congruent. Finally, tan(α)=1/√3, so α=30°.

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Mondrian’s work

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