on a horizontal plane there is a vertical tower with a flag pole on the top of the tower at a point ,9 meters away from foot of the tower ,the angle of elevation of the top and bottom of the flagpole are 60and 30 respectively find the height of the tower and the flag pole mounted on it
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let AB is flagpole and BC as tower
let D is point on ground 9m from foot of ⊥
CD=9m
tan60=AB+BC/9
√3*9=AB+BC.....(1)
tan30=BC/9
1/√3=BC/9
(9*√3)/(√3√3)=BC {rationalize √3}
BC=3√3
put BC in (1)
AB=9√3-3√3=6√3
Height of flagpole=6√3m
height of tower=3√3m
let D is point on ground 9m from foot of ⊥
CD=9m
tan60=AB+BC/9
√3*9=AB+BC.....(1)
tan30=BC/9
1/√3=BC/9
(9*√3)/(√3√3)=BC {rationalize √3}
BC=3√3
put BC in (1)
AB=9√3-3√3=6√3
Height of flagpole=6√3m
height of tower=3√3m
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