From the top of a building 60 m high, the angles

Leave a Comment / Class 10th, trigonometry applications / By Sapling Academy

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° = $\frac{AB}{BQ}$

$\Rightarrow \sqrt 3 = \frac{60}{D}$

$\Rightarrow D = \frac{60}{\sqrt3} = \frac{3 \times 20}{\sqrt3} = 20\sqrt3$

Therefore, the horizontal distance is 20√3 m

(ii) Length of AP:

In Δ ACP, cos P = cos 30° = $\frac{PC}{AP}$

$\Rightarrow \frac{\sqrt3}{2} = \frac{D}{AP} = \frac{20\sqrt 3}{AP}$

$\Rightarrow AP = (20\sqrt 3) \frac {2}{\sqrt 3} = 40$

Therefore, length of AP is 40m.

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