Let a vertical tower `A B` have its end `A` on the level ground. Let `C` be the mid point of `A B` and `P` be a point on the ground such that `A P=2A Bdot` If `/_B P C=beta,` then `tanbeta` is equal to : `2/9` (2) `4/9` (3) `6/7` (4) `1/4`

Options

A. `2/9`
B. `4/9`
C. `6/9`
D. `1/7`

Answer

A

Explanation

Let `angleAPB=theta`

Clearly, `theta=alpha+beta`
`rArr tan theta=tan (alpha + beta)`
`rArr tan theta=(tan alpha + tan beta)/(1-tan alpha tan beta)`
`rArr h/(2h)=((h//2)/(2h) +tan beta)/(1-(h//2)/(2h)xx tan beta)`
`rArr 1/2=(1/4 + tan beta)/(1-1/4 tan beta)`
`rArr 1/2-1/8 tan beta=1/4 + tan beta`
`rArr 1/4 =9/8 tan beta rArr tan beta =2/9`