A vertical lamp-post of height 9 metres stands at the corner of a rectangular field. The angle of elevation of its top from the farthest corner is `30^@`, while from another corner it is `45^@`. The area of the field is

Options

A. `81sqrt2m^2`
B. `9sqrt2m^2`
C. `81sqrt3m^2`
D. `9sqrt3m^2`

Answer

A

Explanation

Let AP be the lamp-post of 9m standing at corner A of the rectangular field ABCD.

In `triangle'sBAP` and CAP, we have
`tan 45^@=(PA)/(BA)` and `tan 306=(PA)/(AC)`
`rArr BA=9m` and `AC=9sqrt3`m
`therefore BC=sqrt(AC^2-AB^2)=sqrt(243-81)=sqrt162=9sqrt2`m
Hence , area of the field `=ABxxBC=9xx9sqrt2m^2=81sqrt2 m^2`