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

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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