Question

A lotus flower is blooming in a lake . The flower is 1/2 metres above the surface of the lake. When the western wind blows, the flower droops at a distance of 2 metres from the base. Find the depth of the lake.and make firure

Answer 1

Answer:

The depth of the lake is 3.75 meters

Step-by-step explanation:

Let AC be the original position of the flower and B represents be water surface and C represents bottom.

As the wind blows the flower realigns in position CD.

let the total length of the flower, AC = CD = x

=> BC = AC -AB = x - 0.5

BD = 2 m(given)

In right angled triangle BCD,

CD² = BC² + BD²

=> x² = (x - 0.5)² + 2²

=> x² = x² - x + 0.25 + 4

=> x = 4.25 m

Hence depth of the lake = BC = x - 0.5 = 4.25 - 0.5 = 3.75 m