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From a point C on the ground, the angle of elevation of the top of a tower is $30 °$ and that of the top of the flag-staff fixed on the top of the tower is $45 ° .$ If the length of the flag-staff is $5 m,$ then the height of the tower is:

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2.83 m

6.83 m

4.83 m

8.83 m

answer is C.

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Detailed Solution

Given, the angle of elevation of the top of the tower is

30 °

.
And the angle of elevation of the top of the flag-staff fixed on the top of the tower is

45 ° .

Consider the figure,
Question Image

We know,

\tan 45 ° = 1

Let x be the distance between point C and tower using tower height. Determine the value of d:

tan 30 ° = h x ⇒ x = h tan 30 ° ⇒ x = h 3 ∵ tan 30 ° = 13

The distance between point C and tower using flag height,

x = h + 5 tan 45 ° ⇒ h 3 = h + 5 ∵ tan 45 ° = 1 ⇒ h (3 − 1) = 5 ⇒ h = 6.83 m

The height of the tower is 6.83 m.
Therefore, option 3 Is correct.

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