Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?

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## Solution

The maximum angle is 45°.

This solution makes clever use of the trigonometric equality tan(x – y)=(tan(x)-tan(y))/(1+tan(x)tan(y)).

## Poem

Don Quixote the man from the Mancha

Poor Hidalgo travelling

With his horse Rosinante

The windmill approaching

For him giants in the wind turning

A lot of adventures happening

Sancho Panca his friend is helping

Morality being out of the real life is destroying