A surveyor on one bank of canal observed the image of the 4 inch and 17 ft marks on a vertical staff,which is partially immersed in the water and held against the bank directly opposite to him, coincides If the `17 ft` mark and the surveyor's eye are both `6 ft` above the water level ,estimate the width of the canal ,assuming that the reflective index of the water is `4//3` .Zero mark is at the bottom of the canal.

Answer

16 feet

Explanation

`(4)/(3)(x)/(sqrt(x^(2) + ((32)/(3))^(2)))= (d-x)/(sqrt(36 +(d+x)^(2)))`
`16x^(2)[36 + (d-x)^(2)] =9 (d-x)^(2)[x^(2) + (1024)/(9)]`
`16 xx 36 x^(2) + 16x^(2)(d-x)^(2) = 9(d-x)^(2)x^(2)+ 1024(d-x)^(2)`
`16 xx 36 (d^(2))/(4) + 16 (d^(2))/(4) xx (d^(2))/(4) = 9 (d^(2))/(4) xx (d^(2))/(4) + 1024(d^(2))/(4)`
` d= sqrt((4)/(7) xx 448 ) = 16`