Q47 of 68 Page 9

The angle of elevation of the top of a tower from the bottom of a tree is 60°, and the angle of elevation of the top of the tree from the foot of the tower is 30°. If the tower is 50 m tall, what is the height of the tree?


Let tree be AB and tower be CD


Given: Height of the tower = 50 m


Hence, CD = 50 m


The angle of elevation of the top of the tower from the bottom of a tree = 60°


Hence, ∠ CBD = 60°


The angle of elevation of the top of the tree from the foot of tower = 30°


Hence, ∠ ADB = 30°


Now, In right ΔCBD, we have





In the right ΔADB, we have







Hence, the height of the tree is


More from this chapter

All 68 →
45

The distance between two vertical pillars is 100 m, and the height of one is double of the other. The angles of elevation of their tops at a point on the line joining the foot of the two pillars are 60° and 30° respectively. Find their heights.

 46

Two pillars of equal height stand on either side of roadway which is 30 m wide. At a point in the roadway between the pillars, the elevations of the tops of the pillars are 60° and 30°. Find the heights of the pillars and the position of the point.

 48

A vertical tower of height 12m subtends a right angle at the top of a flagstaff If the distance between them is 12 m, find the height of the tower.

 49

The angles of elevation of the top of a rock at the top and foot of a 100 m high tower, at respectively 30° and 45°. Find the height of the rock.