# Dedicated to Ayush Rai

Geometry Level 5

A flagstaff is on the top of a tower which stands on a horizontal plane.

A person observes the angles subtended by the flagstaff and the tower at a point on the horizontal plane as $$\alpha$$ and $$\beta$$ respectively.

He then walks a distance $$a$$ towards the tower and observes that the angle subtended by the flagstaff remains unchanged.

Enter the height of the tower correct to three decimal places.

Details and assumptions:

• $$\alpha=15^\circ$$
• $$\beta=30^\circ$$
• $$a=2$$

Clarification figure:

Bonus questions:

• Generalise for arbitrary values of $$\alpha, \beta$$ and $$a$$.
• Find the height of the flagstaff in this generalised situation.
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