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Don Quixote and the windmill

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°.

Solution by Juan Pablo.

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

Bella

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