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The angle of depression of two ships from the top of a light house are 45 and 30 degree, sailing in the same direction. If the height of the light house is 150 m, then what will be the distance between the 2 ships?

The angle of depression of two ships from the top of a light house are 45 and 30 degree, sailing in the same direction. If the height of the light house is 150 m, then what will be the distance between the 2 ships? Correct Answer 150 (√3 – 1) m

Given, Angle of X ship = 45 – degree, angle of Y ship = 30 – degree, height = 150m Let the distance between ship X and glacier be x m, ship Y and glacier be y m. Ship X ➩ tan 45 = height / base distance ➩ 1 = 150 / x ➩ x = 150 m Ship Y ➩ tan 30 = height / base distance ➩ 1 / √3 = 150 / y ➩ y = 150√3 Distance between the two ships = y – x = 150√3 – 150 m = 150 (√3 – 1) m

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