Q17 of 107 Page 12

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


In Δ DBC


tan 45° = h /y


h = y (∵ tan 45° = 1)……….1


In ΔACD


tan 30° =


=


√3 h = 2x + h (from 1)


2x= (√3- 1) h
h =


h = (√3 +1)x meter

More from this chapter

All 107 →
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

 16

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

 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

 19

The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =