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:
Aptitude
Height and Distance
Difficulty: Medium
Choose an option
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A100(√3 + 1) m
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B100(√3 - 1) m
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C200 m
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D100√3 m
Answer
Correct Answer: 100(√3 + 1) m
Explanation
Given
- Height of lighthouse, H = 100 m
- Angles of elevation from the two ships: 30° and 45°
- Ships are on opposite sides of the lighthouse
Step 1: Horizontal distance of ship with 30°\tan 30^\u00b0 = 𝐻 𝑑 1 d 1 H ⇒ 1 3 3 1 = 100 𝑑 1 d 1 100 d 1 1 = 100 3 3 m
Step 2: Horizontal distance of ship with 45°\tan 45^\u00b0 = 𝐻 𝑑 2 d 2 H = 1 ⇒ d 2 2 = 100 m
Step 3: Distance between shipsOpposite sides ⇒ total separation = d 1 1 + d 2 2 = 100 3 3 + 100 = 100(\u221A3 + 1) m