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From the top of a building 15 m high, the angle of elevation of the top of a tower is found to be $30 °$ . From the bottom of the same building, the angle of elevation of the top of the tower is found to be $60 °$ . Determine the height of the tower and the distance between the tower and the building.

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24.5 m

23.5 m

25.5 m

22.5 m

answer is A.

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Detailed Solution

Given that from the top of a building 15 m high, the angle of elevation of the top of a tower is found to be

30 °

. From the bottom of the same building, the angle of elevation of the top of the tower is found to be

60 o .

We have to find the height of the tower and distance between and tower.

In a right-angle triangle, tan θ = Opposite side Hypotenuse .

△ O D C,

⇒ tan C = O D D C ⇒ tan 30 o = O D D C ⇒ 13 = h x ⇒ x = 3 h

△ O A B,

⇒ tan B = A D + D O A B ⇒ tan 60 o = h + 15 x ⇒ 3 = h + 15 x ⇒ 3 = h + 15 3 h ⇒ 3 h = h + 15 ⇒ 2 h = 15 ⇒ h = 7.5 ⇒ x = h 3 ⇒ x = 7.5 3

Thus, the height of the tower is,

O A = h + 15 ∴ O A = 22.5

Therefore, the height of the tower is 22.5 m and the distance is

7.5 3

m.
Therefore, the correct option is 1.

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