Question

Question 9
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation 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.

Answer 1

Let CD be the height of the tower equal to 50 m.
Let AB be the height of the building.
BC be the distance between the foot of the building and the tower.
Elevations are 30° and 60° from the tower and the building respectively.
As per question,

In right ΔBCD,
tan 60°=CD/BC
⇒√3=50/BC
⇒BC=50√3m
Also,
In right ΔABC,
tan 30°=AB/BC
⇒1/√3=AB/BC
⇒AB=50/3m
Thus, the height of the building is 50/3m.