Home
Class 10
MATHS
The angle of elevation of the top of a t...

The angle of elevation of the top of a tower from two distinct points s and t from foot are complementary. Prove that the height of the tower is `sqrt[st]`.

Text Solution

Verified by Experts

Let BC be a tower of height 'h'. Let `AC=s" and "DC=t`. From points A and D, the angle of elevation of top B of the tower are complementary.
Let `angleBAC=theta`
`:. angleBDC=90^(@)-theta`
In `DeltaBAC`
`tantheta=(BC)/(AC)=h/s …(1)`
In `DeltaBDC`
`tan(90^(@)-theta)=(BC)/(CD)rArrcottheta=h/t`
`rArr 1/(tantheta)=h/trArrs/h=h/t" [from(1)]`
`rArr h^(2)=strArrh=sqrt(st)`
`:. " height of the tower "=sqrt(st)`
Promotional Banner

Topper's Solved these Questions

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise|32 Videos

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Revision Exercise (short Answer Questions)|5 Videos

  • REAL NUMBERS

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

  • STATISTICS

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

Similar Questions

Explore conceptually related problems

The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is sqrt(st) .

If the angles of elevation of the top of a tower from two points distance s and t(s gt t) from its foot are 30° and 60° respectively, then the height of the tower is

The angle of elevation of the top of a tower from two points on the ground at distances a metres and b metres from the base of the tower and in the same straight line are complementary.Prove that height of the tower is sqrt(ab).

The angle of elevation of the top of a tower at a point on the ground, 50 m away from the foot of the tower, is 60°. Find the height of the tower.

The angle of elevation of the top of a tower from a point on the ground,which is 30m away from the foot of the tower is 30o. Find the height of the tower.

If the angle of elevation of the top of a tower from a point distant 100 m from its base is 45^(@) , then find the height of the tower.

The angle of elevation from two points at a distance of x and y from the feet of a Tower are complementary, the height of the Tower is

The angle of elevation of the top of a tower from a point 40 m away from its foot is 60^(@) . Find the height of the tower.

The angle of elevation of the top of a tower from the point P and Q at distance of a and b respectively from the base of the tower and in the same straight line with it are complementary .The height of the tower is