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.

A path separates two walls. A ladder leaning against one wall rests at

1.	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.
Answer» 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^@` `=>PE = x/sqrt2 = (60sqrt3)/(sqrt2) = 30sqrt6m = 73.47 m` So, the required height is `73.47m.`