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Q.

On a horizontal plane, there is a vertical tower with a flag pole on the top of the tower. At a point 9 m away from the foot of the tower the angles of elevation of the top and bottom of the flag pole are $60 °$ and $30 °$ respectively. Find the heights of the tower and flag pole mounted on it.

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a

10.4 m and 4.2 m

b

9.4 m and 5.2 m

c

10.4 m and 5.2 m

d

11.4 m and 5.2 m

answer is C.

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Detailed Solution

Given that there is a vertical tower with a flag pole on the top of the tower.
We have to find the heights of the tower and flag pole mounted on it.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for can be expressed as:

tan θ = opposite adjacent

Suppose the height of the flag pole and tower be AB and BC.
Then, by using the figure geometry,
Question Image

Question Image

In triangle A C D tan 60 ° = A C D C ⇒ 3 = A C 9 ⇒ A C = 93 m

tan 30 ° = B C D C ⇒ 13 = B C 9 ⇒ B C = 93 ⇒ B C = 33 m

Or

⇒ B C = 3 (1.732) ∴ B C = 5.2 m

Thus, the height of the flag pole is,

A B = A C − B C ⇒ A B = 93 − 33 ⇒ A B = 63 m

⇒ A B = 6 (1.732) ∴ A B = 10.4 m

The height of the flag pole and tower is 10.4 m and 5.2 m.
Therefore, the correct option is 3.

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On a horizontal plane, there is a vertical tower with a flag pole on the top of the tower. At a point 9 m away from the foot of the tower the angles of elevation of the top and bottom of the flag pole are 60 ° and 30 ° respectively. Find the heights of the tower and flag pole mounted on it.