**Q) From the top of a building 60 m high, the angles of depression of the top and bottom of the vertical lamp post are observed to be 30° and 60° respectively.(i) Find the horizontal distance between the building and the lamp post.(ii) Find the distance between the tops of the building and the post.**

**Ans: **

Let’s start with the diagram for this question:

Here we have tower AB of 60m height and PQ as lamppost.

Angle of depression from A to P and Q are given.

We need to find distance D and length AP.

Let’s make a simplified diagram of the same for our better understanding:

**(i) Horizontal distance between tower & lamp post:**

In Δ ABQ, tan Q = tan 60° =

**Therefore, the horizontal distance is 20√3 m**

**(ii) Length of AP:**

In Δ ACP, cos P = cos 30° =

**Therefore, length of AP is 40m.**

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