The angles of depression of two points from the top of the tower are `30^(@) and 60^(@)`. IF the height of the tower is 30 m, then find the maximum possible distance between the two points.

Options

A. `40sqrt3` m
B. `30sqrt3` m
C. `20sqrt3` m
D. `10sqrt3` m

Answer

A

Explanation

For the maximum possible distane, two points lie on either side of the tower.
Let AB be the height of the tower.
AB = 30 m (given)
Let P and Q be the given points
In `DeltaABP`,

`tan30^(@)=(AB)/(PB)rArr(1)/(sqrt3)=(30)/(PB)rArrPB=30sqrt3`.
`In DeltaABQ, tan60^(@)=(AB)/(BQ)`
`rArrsqrt3=(30)/(BQ)rArrBQ=(30)/(sqrt3)`m.
Now, PQ =PB+BQ
`=30sqrt3+(30)/(sqrt3)=30(sqrt3+(1)/(sqrt3))`
`30((4)/(sqrt3))=40sqrt3` m.