Question

From the top of a lighthouse, $100$ $m$ above sea level, the angle of depression of a ship, sailing towards it, changes from ${30}^{\circ }$ to ${45}^{\circ }.$ Determine the distance travelled by the ship during the period of observation.

Answer 1

The height of tower is $100m$

The angle of depression (initial) $={30}^{\circ }$

The distance from tower is $\tan 30=\frac{distance}{Height}\frac{1}{\sqrt{3}}=\frac{Distance}{100}Distance=\frac{100}{\sqrt{3}}m$

The angle of depression (final) $={45}^{\circ }$

The distance from tower is $\tan 45=\frac{distance}{Height}1=\frac{Distance}{100}Distance=100m$

The distacne covered is $100-\frac{100}{\sqrt{3}}100-57.73=42.27m$