As observed from the top of a light house, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30∘to40∘. Determine the distance travelled by the ship during the period of observation.

Question

Filo · Accepted Answer

Let A and B be the two positions of the ship. Let d be the distance travelled by the ship during the period of observation i.e. AB = d metres.
Let the observer be at O, the top of the lighthouse PO.
It is given that PO = 100 m and the angle of depression from O of A and B are

3 0^{\circ}

and

4 5^{\circ}

respectively.

∴ ∠ O A P = 3 0^{\circ} an d ∠ OBP = 4 5^{\circ}

In

Δ

OPB, we have

t an 4 5^{\circ} = \frac{OP}{BP}

\Rightarrow 1 = \frac{100}{BP}

\Rightarrow

BP = 100 m
In

Δ

OPA, we have

\Rightarrow t an 3 0^{\circ} = \frac{OP}{A P}

\Rightarrow \frac{1}{3} = \frac{100}{d + BP}

\Rightarrow

d + BP = 100

3

\Rightarrow

d + BP = 100

3

\Rightarrow

d = 100

3

- 100

\Rightarrow

d = 100(

3

- 1) = 100(1.732 - 1) = 73.2 m.
Hence, the distance travelled by the ship from A to B is 73.2 m.

Question Text	As observed from the top of a light house, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from $3 0^{\circ} t o 4 0^{\circ}$ . Determine the distance travelled by the ship during the period of observation.
Answer Type	Text solution:1
Upvotes	150

As observed from the top of a light house, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from $3 0^{\circ} t o 4 0^{\circ}$ . Determine the distance travelled by the ship during the period of observation.

Text solutionVerified

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