`ABC` is a triangle in vertical plane. Its two base angles `angleBAC` and `angleBCA` are `45^(@)` and `tan^(-1) (1//3)` respectively. A particle is projected from point A such that it passes through vertices `B` and `C`. Find angle of projection in degrees:

Options

A. `60^(@)`
B. `53^(@)`
C. `tan^(-1)(5//4)`
D. `tan^(-1)(5//3)`

Answer

B

Explanation

equation `y=x tantheta(1-(x)/(R))`
at `B x=y`
`tantheta=(R)/(R-Y)` .....(i)
`tan45^(@)=(Y)/(X)`
`x=y` .....(ii)
`((1)/(3))=(Y)/(R-x)` ....(iii)
Solving equation `2` and `3`
`R=4y=4x` {it om (i)
`tantheta=(R)/(R-(R)/4)`
`tantheta=(4)/(3)`
`theta=53^(@)`