Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

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Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A. 173 m

B. 200 m

C. 273 m

D. 300 m

Correct Answer :

C. 273 m

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

Then, AB = 100 m, ACB = 30° and ADB = 45°.
$\frac{A B}{A C} = \tan 30 ° = \frac{1}{\sqrt{3}} \Rightarrow A C = A B \times \sqrt{3} = 100 \sqrt{3} m \frac{A B}{A D} = \tan 45 ° = 1 \Rightarrow A D = A B = 100 m C D = (A C + A D) = (100 \sqrt{3} + 100) m = 100 (\sqrt{3} + 1) m = (100 x 2.73) m = 273 m .$

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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

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A. 30º

B. 45º

C. 60º

D. 90º

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Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A. 173 m

B. 200 m

C. 273 m

D. 300 m

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A. 2.3 m

B. 4.6 m

C. 7.8 m

D. 9.2 m

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A. 149 m

B. 156 m

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A. 21.6 m

B. 23.2 m

Discuss this answer

Answer 1

A. 8 units

Answer 2

B. 12 units

Answer 3

C. None of these

Answer 4

D. Data inadequate

Answer 5

C. 24.72 m

Answer 6

D. None of these

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Correct Answer :

Show all Height and Distance MCQ

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