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In the figure given, from the top of a building AB=60 m high t

Question

In the figure given, from the top of a building AB $= 60 m$ high the angles of depression of the top and bottom of a vertical lamp post $C D$ are observed to be $3 0^{\circ}$ and $6 0^{\circ}$ respectively. Find: (i) The horizontal distance between $A B$ and $C D$ . (ii) The height of the lamp post $C D$ .

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In the figure given, from the top of a building AB

= 60 m

high the angles of depression of the top and bottom of a vertical lamp post

C D

are observed to be

3 0^{\circ}

and

6 0^{\circ}

respectively. Find: (i) The horizontal distance between

A B

and

C D

. (ii) The height of the lamp post

C D

7 mins ago

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Text solutionVerified

Given:

A B = 60 m

∵ ∠ P A C = 6 0^{\circ}

∴ ∠ P A C = ∠ BC A

(i) Now in

Δ A BC

tan 6 0^{\circ} = \frac{A B}{BC}

3 = \frac{60}{BC}

\Rightarrow BC = \frac{60}{3} \times \frac{3}{3}

BC = \frac{60 3}{3} = 203

Hence, the horizontal distance between

A B

and

C D = 203 m

.
(ii) Let

A E = x

and proved above

BC = 203 m

∴ BC = E D = 203

Now in

Δ A E D

tan 3 0^{\circ} = \frac{A E}{E D}

\frac{1}{3} = \frac{A E}{20 3}

\Rightarrow 3 A E = 203

\Rightarrow A E = 20 m

now

EB = A B - A E

∴ EB = 60 - 20 = 40 m

∴ EB = C D

∴ C D = 40 m

Hence, the height of the lamp post

= 40 m

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Question Text	In the figure given, from the top of a building AB $= 60 m$ high the angles of depression of the top and bottom of a vertical lamp post $C D$ are observed to be $3 0^{\circ}$ and $6 0^{\circ}$ respectively. Find: (i) The horizontal distance between $A B$ and $C D$ . (ii) The height of the lamp post $C D$ .
Answer Type	Text solution:1
Upvotes	150