Q) 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, then find the height of the building.

Ans:

Step 1: Diagram for this question:

Let AB be the tower of 50 m height and PQ be the building of H m.

The distance between the building and the tower be D m, and angle of elevations be as shown in the image above.

Step 2: Find the distance D:

In Δ ABQ, tan 60 =

∴  D =  

Step 3: Find the height H:

Now in Δ PQB, tan 30 =

H =

or H = m

Therefore, the height of the building is m.