Question

A man standing on a ship approaching the port towards the lighthouse is observing the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the lighthouse changes from α to β. Then:

Options

• α > β

• α < β

• α = β

• α ≤ β

Answer 1

α < β

Explanation:

As the ship approaches the lighthouse the horizontal distance to the lighthouse decreases while the lighthouse height stays the same. Since tan (angle) = height / horizontal distance, the tangent and therefore the angle increases when distance decreases, so the later angle β is larger than the earlier angle α.