Q16 of 25 Page 9

A window of house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite site of the lane are found to be α and β respectively. Prove that the height of the other house is h (1+ tanα cotβ).

To Prove:


The height of another house = h (1+ tanα cotβ)


Formula Used:



Explanation:


A is the window which is h metres above ground that is AD = h


BC is the house with B as top of house and C as bottom.


The angle of elevation and depression are:


∠BAE = α and ∠EAC = β



From figure EC = AD = h


Consider ΔACE




Now consider ΔAEB



Using (i)




As


⇒ BE = h(tanα)(cotβ)


From figure


BC = BE + EC


⇒ BC = h(tanα)(cotβ) + h


⇒ BC = h(1 + tanαcotβ)


BC is the height of house which is h(1 + tanαcotβ)


Hence proved


More from this chapter

All 25 →
14

A statue 1.6 m tall stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

 15

The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

 17

The pillars of equal height stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars, the elevation of the top of the pillar are 60° and 30° . Find the height of the pillars and the position of the point.

 18

As observed from the top of a lighthouse, 200 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation.