Home
Class 10
MATHS
A vertical tower stands on a horizontal ...

A vertical tower stands on a horizontal plane and is surmounted by vertical flagstaff to height 6m. At a point on the plane, the anglea elevation of the bottom of flagsteff is `30^(@)` and that of the top of the flagstaff is `60^(@)`. Find the height of the tower. [Use `sqrt(3) = 1.732`]

Text Solution

Verified by Experts

The correct Answer is:
`3 m`
`(OA)/(AB) = cot 30^(@) rArr (OA)/(h m) = sqrt(3) rArr OA = hsqrt(3) m "…….."(i)`
`(OA)/(AC) = cot 60^(@) rArr (OA)/((h+6) m) = 1/(sqrt(3)) rArr OA = ((h+6))/(sqrt(3)) m"………"(ii)`
`:. hsqrt(3) = ((h+6))/(sqrt(3)) rArr 3h= h+ 6`.
`rArr 2h = 6 rArr h = 3`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A vertical tower stands on a horizontal plane and is surmounted by a flag-staff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flag-staff is 30o and that of the top of the flag-staff is 45o . Find the height of the tower.

A vertical tower stands on a horizontal plane and surmounted by a flagstaff of height 'h'. At a point on the plane. The angle of elevation of bottom of the flagstaff is alpha and that of the top of the flagstaffis beta . Find the height of the tower :

A vertical tower stand on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres.At a point on the plane,the angles of elevation of the bottom and the top of the flag-staff are respectively 30^(0) and 60^(0) . Find the height of the tower.

A vertical tower stands on a horizontal land and is surmounted by a vertical flag staff of height 12 metres. At a point on the plane, the angle of elevation of the bottom and the top of the flag staff are respectively 45° and 60°. Find the height of tower.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height 6 meters. At point on the plane, the angle of elvation of the bottom and the top of the flag are respectively 30^@ and 60^@ . Find the height of tower

A vertical tower of height 20 m stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom and top of flag staff are 45^(@) and 60^(@) , respectively. Find the value of h.

A vertical tower sands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane,the angles of elevation of the bottom and the top of the flagstaff are alpha and beta .Prove that the height of the tower (h tan alpha)/(tan beta-tan alpha)

A vertical tower Stands on a horizontal plane and is surmounted by a vertical flag staff of height h.At a point on the plane,the angles of Elevation of the bottom and the top of the flag staff are alpha and beta respectively Prove that the height of the tower is (h tan alpha)/(tan beta-tan alpha)