Q27 of 28 Page 93

On one side of a road a tower is situated and on the other side a house in situated. The angles of depression of the root of the house and base of the house from the top of the tower are respectively 45° and 60°. If the height of the house is 12 m then find the height of the tower. (√3 = 1.732)


Let Height of the House CD, Height of the Hill is AB.


Given, CD = 12, AE = 12


∠BCE = 30o


∠BDA = 600


In ∆ABD,



AD√3 = BE + 12


………..(1)


In ∆BCE,



EC = BE…………..(2)




BE + 12 = BE√3


12 = BE(√3 – 1)



BE = 6(√3 + 1)


Height of the tower = BE + AE = 6√3 + 6 + 12


= 28.39


More from this chapter

All 28 →
24

A 12 m high tree breaks due to wind such that its top touches the ground and makes an angle of 60° with the ground. Find at what height from the earth has the tree broken by the wind (√3 = 1.732)?

 25

A highway passes through the foot of a tower. A man observes a car at an angle of depression of 30° from the top of the tower. That car is approaching the foot of the tower. Six seconds later, the angle of depression of the car becomes 60°. In what time will the car pass through the foot of the tower?

 26

The angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are supplementary. Prove that the height of the tower is 6m.

 28

If the angle of elevation of the Sun changes from 30° to 60°. Then find the difference in the length of the shadows of a 15 m high pillar at both these angles of elevation.