15. The height of an observation tower is$180m$ above sea level. A ship coming towards the tower is observed at an angle of depression of ${{30}^{\circ }}$. Calculate the distance of the boat from the foot of the observation tower.

Home » 15. The height of an observation tower is above sea level. A ship coming towards the tower is observed at an angle of depression of . Calculate the distance of the boat from the foot of the observation tower.

15. The height of an observation tower is $180m$ above sea level. A ship coming towards the tower is observed at an angle of depression of ${{30}^{\circ }}$ . Calculate the distance of the boat from the foot of the observation tower.

Class 10 | Frank | Heights and Distances | ICSE | Maths

15. The height of an observation tower is $180m$ above sea level. A ship coming towards the tower is observed at an angle of depression of ${{30}^{\circ }}$ . Calculate the distance of the boat from the foot of the observation tower.

As per data given in the question,

Let us assume that PQ be the observation tower with height $180m$ above sea level and R be the position of the ship.

Also assume that the distance of the boat from the foot of the observation tower be ‘x’m.

Consider the ΔPQR,

$\tan \theta =\frac{PQ}{RQ}$

$\tan {{30}^{\circ }}=\frac{180}{x}$

As we know, $\tan {{30}^{\circ }}=\frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{3}}=\frac{180}{x}$

$x=\frac{180}{\sqrt{3}}$

$x=\frac{180}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$

$x=60\sqrt{3}m$

$x=311.76m$

Hence, the total distance of the boat from the foot of the observation tower is $311.76m$

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