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Two fishes are swimming in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse from the two fishes is 30 degree and 45 degree. If the lighthouse is 200 m high, what is the distance between the two fishes?

Two fishes are swimming in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse from the two fishes is 30 degree and 45 degree. If the lighthouse is 200 m high, what is the distance between the two fishes? Correct Answer 200 (1 + √3) m

Given, Height = 200m, fish A angle = 30, fish B angle = 45 Let the distance from fish A to lighthouse = x m, from fish B to lighthouse = y m. Fish A ➩ tan 30 = height / base distance ➩ 1 / √3 = 200 / x ➩ x = 200√3 m Fish B ➩ tan 45 = height / base distance ➩ 1 = 200 / y ➩ y = 200 m Total distance = 200√3 + 200 = 200 (1 + √3) m

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