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Let a vertical tower AB have its end A o...

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 `sqrtBPC = beta`, then tan `beta` is equal to

A

`(6)/(7)`

B

`(1)/(4)`

C

`(2)/(9)`

D

`(4)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let AB = h, then AP = 2h
and AC = B C = `(h)/(2)`
Again, let `angleCPA = alpha`

Now, in `angleABP, tan (alpha+beta)=(AB)/(AP) = (h)/(2h)=(1)/(2)`
Also, in `DeltaACP, tan alpha = (AC)/(AP) = (2)/(2h) = (1)/(4)`
Now, `tanbeta = tan[(alpha+beta)-alpha]`
`=(tan(alpha+beta)-tanalpha)/(1+tan(alpha+beta)tanalpha)=((1)/(2)-(1)/(4))/(1+(1)/(2)xx(1)/(4))=((1)/(4))/((9)/(8))=(2)/(9)`
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