Question

A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches a height of 9 m on the wall and makes an angle of 60 degrees with the ground. If while resting at the same point on the path, it were made lean against the other wall, it would have made an angle of 45 degrees with the ground. Find the height it would have reached on the second wall.

Answer 1

walls= AB and CD

lenght of ladder = x

height = h

in ΔAOB  

sin 60 = AB/ AO

√3/2 = 90/x

x= 180/√3

In ΔCOD

sin 45= CD/CO

1/√2 = h/x

1/√2 = h/ 180/√3

h= 180/√6 x √6/√6

h= 30√6

h= 73.47