**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.

**A****ns:**

**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.**