Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If `sqrt(BPC = beta`, then tan `beta` is equal to

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`