Question

A tower subtends angles `alpha,2alpha,3alpha` respectively, at point `A , B ,a n dC` all lying on a horizontal line through the foot of the tower. Prove that `(A B)/(B C)=1+2cos2alphadot`

Answer 1

`/_APB=/_PBC-/_BAP`
`2alpha-alpha`
`/_APB=alpha`
`/_BPC=alpha`
`BP=AB`
Using Sin formula for triangle BCP
`(BC)/(sinalpha)=(AB)/(sin(180-3alpha))`
`(AB)/(BC)=(sin3alpha)/sinalpha`
`=(3sinalpha-4sin^3alpha)/sinalpha`
`(AB)/(BC)=3-4sin^2alpha`
`=3-4((1-cos2alpha)/2)`
`(AB)/(BC)=1+2cos2alpha`.