AB is the distance from bottom of a kind to a lotus and above the water has thr measure AE=3 dm. Then, there is a sparrow perched on the lotus flower and make it lean by direction BA', where EA'=9 dm. Find the depth of the EB.
AB is the distance from bottom of a kind to a lotus and above the water has thr measure AE=3 dm. Then, there is a sparrow perched on the lotus flower and make it lean by direction BA', where EA'=9 dm. Find the depth of the EB.
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To find the depth of EB, we can consider the triangle AEB formed by the sparrow, the lotus flower, and the point right below the lotus in the water.
From the given information, we have AE = 3 dm, EA' = 9 dm, and EA = 3 dm. We can form a right triangle AEA' with AE = 3 dm, EA' = 9 dm, and AA' = 6 dm (since EA' = EA + AA').
Now, let's find AA' by using the Pythagorean theorem:
AA'^2 = AE^2 + EA'^2
AA'^2 = 3^2 + 9^2
AA'^2 = 9 + 81
AA'^2 = 90
AA' = sqrt(90)
AA' = 3 sqrt(10) dm
Therefore, the distance AA' = 3 sqrt(10) dm.
In triangle AEB, we have EA = 3 dm, AB = 3 dm (given), and AA' = 3 * sqrt(10) dm. We can find the depth of EB (denoted as x) using the Pythagorean theorem:
AB^2 = EA^2 + EB^2
3^2 = 3^2 + x^2
9 = 9 + x^2
x^2 = 0
x = 0 dm
Therefore, the depth of EB is 0 dm, indicating that the point B lies on the water surface just below the lotus flower.