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The angle of elevation of a tower CD at a place A due south of

Question

The angle of elevation of a tower $C D$ at a place $A$ due south of it is $6 0^{o}$ and at a place $B$ due west of $A$ , the elevation is $3 0^{o}$ . If $A B = 3 K M$ , height of the tower is

45 K M

\frac{2 2}{3 3} K M

\frac{3 3}{2 2} K M

\frac{3 6}{2} K M

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The angle of elevation of a tower

C D

at a place

A

due south of it is

6 0^{o}

and at a place

B

due west of

A

, the elevation is

3 0^{o}

. If

A B = 3 K M

, height of the tower is

7 mins ago

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7 mins ago

Text solutionVerified

Let CE

=

x km

=

= 3

Height of the tower

=

+

= x + 3

Δ

ACD,

tan 60

-opposite adjacent

tan 60 = \frac{C D}{A D}

3 = \frac{x + 3}{A D}

A D = \frac{x + 3}{3}

……….

(1)

Δ

CBE,

tan 30 = \frac{o pp os i t e}{a d ja ce n t} = \frac{CF}{BE}

\frac{1}{3} = \frac{x}{A D}

[∵ BE = A D]

A D = x 3

……….

(2)

From

(1)

and

(2)

x 3 = \frac{x + 3}{3}

3 x = x + 3

3 x - x = 3

2 x = 3

x = \frac{3}{x}

Height of tower

= x + 3

= \frac{3}{2} + 3 = \frac{3 + 6}{2}

= \frac{9}{2}

= 4.5

∴

Height of tower

= 4.5

km.

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Question Text	The angle of elevation of a tower $C D$ at a place $A$ due south of it is $6 0^{o}$ and at a place $B$ due west of $A$ , the elevation is $3 0^{o}$ . If $A B = 3 K M$ , height of the tower is
Answer Type	Text solution:1
Upvotes	150

The angle of elevation of a tower CD at a place A due south of it is 60o and at a place B due west of A, the elevation is 30o. If AB=3KM, height of the tower is

Text solutionVerified

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The angle of elevation of a tower $C D$ at a place $A$ due south of it is $6 0^{o}$ and at a place $B$ due west of $A$ , the elevation is $3 0^{o}$ . If $A B = 3 K M$ , height of the tower is