wo ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. . If the lighthouse is 100 m high, the distance between the two ships are::
Question
wo ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. . If the lighthouse is 100 m high, the distance between the two ships are::
Solution
To solve this problem, we need to use the concept of trigonometry.
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Let's denote the distance between the lighthouse and the first ship as 'a' and the distance between the lighthouse and the second ship as 'b'. The distance between the two ships will be 'a + b'.
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From the problem, we know that the angle of elevation from the first ship to the top of the lighthouse is 30°. This forms a right triangle, where the height of the lighthouse is the opposite side and 'a' is the adjacent side. So, we can use the tangent of the angle to find 'a'.
tan(30°) = height / a a = height / tan(30°) a = 100m / tan(30°) a = 100m / 0.577 = 173.21m
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Similarly, we can find 'b' using the angle of elevation from the second ship, which is 45°.
tan(45°) = height / b b = height / tan(45°) b = 100m / tan(45°) b = 100m / 1 = 100m
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Finally, the distance between the two ships is 'a + b' = 173.21m + 100m = 273.21m.
So, the distance between the two ships is approximately 273.21 meters.
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