As observed from the top of a light-house, 100 $m$ high above sea level, the angle ofdepression of a ship, sailing directly towards it, changes from $30^{\circ}$ to $60^{\circ}$ . Determine the distance travelled by the ship during the period of observation. (Use $\sqrt{3} = 1.732$ )

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Solution

distance travelled $= \frac{100}{tan 30} - \frac{100}{tan 60}$
$= 100 \sqrt{3} - \frac{100}{\sqrt{3}}$
$= 115.46 m$

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As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from $30^{\circ} t o 60^{\circ}$ . Determine the distance travelled by the ship during the period of observation. [Take $\sqrt{3} = 1.732.$ ]