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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 from the two ships is 30 degree and 60 degree. What is the relationship between the distances of the 2 ships from the light house?

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse from the two ships is 30 degree and 60 degree. What is the relationship between the distances of the 2 ships from the light house? Correct Answer x = 3y

Given, Angle from ship 1 = 30 – degree, ship 2 = 60 – degree Let the base distance of ship 1 = x m, ship 2 = y m, height of lighthouse = h m. Ship 1 ➩ tan 30 = height / base distance ➩ 1 / √3 = h / x ➩ x / √3 = h Ship 2 ➩ tan 60 = height / base distance ➩ √3 = h / y ➩ h = y√3 On equating both the equations; ➩ x / √3 = y√3 ➩ x = 3y

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