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

Correct answer: C. 273 m

  • A. 173 m
  • B. 200 m
  • C. 273 m
  • D. 300 m

Explanation

The ships are on opposite sides, so their distances from the lighthouse foot are added: 100 m ÷ tan 30° ≈ 173 m and 100 m ÷ tan 45° = 100 m, giving about 273 m. A student may choose 173 m by calculating only the distance of the ship viewing the lighthouse at 30°.

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