The angle of elevation of the bottom of a window 10 m above the ground level from a point on the ground is `30^@` A pole projecting outwards from the bottom of the window makes an angle of `30^@` with the wall. If the angle of elevation of the top of the pole observed from the same point on the ground is `60^@`, find the length of the pole to the nearest whole number.

Explanation

Let BCE is a wall and C is the foot of window CD which is 10 m above the ground.
`angleBAC+angleACB+angleABC=180^(@)` (angle sum property)
`rArr angleACB=60^(@)`
Also,
`angleACB+angleACF+angleFCE=180^(@)` (linear pair of angles)
`rArr 60^(@)+angleACF+30^(@)=180^(@)rArr angleACF=90^(@)`
In right `Delta ABC`,
`sin30^(@)=(BC)/(AC)rArr1/2=10/(AC)rArrAC=20m`
`:." In eight "DeltaACF`,
`tan30^(@)=(CF)/(AC)rArrCF=ACtan30^(@)`
`rArr CF=20xx1/sqrt3=(20sqrt3)/3m.