As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Asked by Pragya Singh | 1 year ago |  182

1 Answer

Solution :-

Let AB be the lighthouse of height 75 m. Let C and D be the positions of the ships.

30° and 45° are the angles of depression from the lighthouse.

Draw a figure based on given instructions:

To Find: CD = distance between two ships

Step 1: From right triangle ABC,

tan 45° = \( \dfrac{AB}{BC}\)

1= \( \dfrac{75}{BC}\)

BC = 75 m

Step 2: Form right triangle ABD,

tan 30° = \( \dfrac{AB}{BD}\)

 \( \dfrac{1}{\sqrt{3}}=\) \( \dfrac{75}{BD}\)

BD = \(75 \sqrt{3}\)

Step 3: To find measure of CD, use results obtained in step 1 and step 2.

CD = BD – BC = (\( 75 \sqrt{3}-75\)

\( 75(\sqrt{3}-1)\)

The distance between the two ships is \( 75(\sqrt{3}-1)\;m\).

Answered by Abhisek | 1 year ago

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