Multiple choice

Two ships are sailing in the sea on either side of a light-house, The angle of depression of the two ships are $\displaystyle 45^{\circ}$ each. if the height of the light-house is $300$ m, then the distance between ships is :

  1. $600$ m
  2. $\displaystyle 600\sqrt{3}$ m
  3. $\displaystyle 300\sqrt{3}$ m
  4. $300$ m
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A Correct answer
Explanation

The lighthouse height is 300m. The angle of depression is 45 degrees, meaning the distance from the lighthouse to each ship is 300m * cot(45) = 300m. Total distance = 300 + 300 = 600m.

AI explanation

Using the basic trigonometric ratio for angle of depression, the horizontal distance of each ship from the lighthouse equals the height divided by the tangent of the angle. This gives a distance of 300 divided by tan(45), which is 300 m, for each ship. Since the ships are on either side of the lighthouse, the total distance between them is the sum of their individual distances, giving 300 + 300 = 600 m.

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