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A path separates two walls. A ladder lea...

A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches 90m on the wall and makes an angle of `60^@` degree with the ground. If while resting at the same point on the path, it were made to lean against the other wall it would have made an angle of `45^@` with the ground. Find the height it would have reached on the second wall.

Text Solution

Verified by Experts

We can draw a diagram with the given details.
Please refer to video to see the diagram.
From the diagram,
In `Delta ABC`,
`(AB)/(BC) = sin60^@ =>AB = BC sin60^@`
`=>90 = x(sqrt3/2) =>x = 180/sqrt3 = 60sqrt3m`
Now, in `Delta CDE`,
`=>(PE)/(CE) = sin45^@ =>PE = CEsin45^@`
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