Q16 of 107 Page 12

It is found that on walking x meters towards a chimney in a horizontal line through its base, the elevation of its top changes from 30° to 60°. The height of the chimney is


Here AB is the chimney of height h


By walking x meters toward chimney the angle of elevation changes from 30° to 60°


In Δ ABH


tan 60° =


h = √3 y


= y …………….1


In Δ ABG


tan 30° =


=


√3 h = x+y


√3 h - = x (from 1)


= x


h =

More from this chapter

All 107 →
14

The angle of elevation of a cloud from a point h metre above a lake is θ. The angle of depression of its reflection in the lake is 45°. The height of the cloud is

 15

A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is

 17

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun’s elevation is 30° than when it was 45°. The height of the tower in metres is

 18

Two poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is