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There are two vessels in the sea, opposite side of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the vessel  is 30° and 45°, respectively. Then, what is the distance between the two vessel, if the lighthouse is 120 m high?

There are two vessels in the sea, opposite side of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the vessel  is 30° and 45°, respectively. Then, what is the distance between the two vessel, if the lighthouse is 120 m high? Correct Answer 120(1 + √3) m

Given:

Height of lighthouse = 120 m

Formula Used:

Calculation:

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With help of the data given in the question, above diagram can be represented.

Suppose AB is the height of the lighthouse.

In ΔABC, ∠ACB = ∠CBA = 45°

∴ CA = AB = 120 m

In ΔABD, ∠ADB = 30°

⇒ tan30° = AB/AD

⇒ 1/√3 = 120/AD

⇒ AD = 120√3

∴The distance between two vessels (CD) = AC + AD = 120 + 120√3

⇒ 120(1 + √3) m

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