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Wedge on Wedge

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

We contruct a new triangle as shown. Angle $x$ is equal to $90^\circ - (90^\circ - y) = y$, so the highlighted triangles are similar. Therefore $$p = 48 \times \frac{39}{52} = 36$$ $$q =20\times \frac{39}{52} = 15$$

The base is split $48 - q : q = 33 : 15 = 11 : 5$ and the ball falls a distance of $p + 20 = 36 + 20 = 56$.