# Calculus

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The captain of a ship at sea sights a lighthouse which is 260 feet tall.

The captain measures the the angle of elevation to the top of the lighthouse to be 21.

How far is the ship from the base of the lighthouse?

• trigonometry -

Assuming a flat Earth, it is given by

H/X = tan 21 = 0.3839

where H = 260 feet and X is the distance to the lighthouse

So X = 677 feet

Too close for comfort.

The curvature of the Earth is negligible over such a short distance.

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