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The two palm trees are of equal heights and are standing opposite each other on either side of the river, which is 80 m wide. From a point O between them on the river the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees.

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Height = 34.6 m and the distance of point O from the tress is 20m and 60m.

Height = 24.6 m and the distance of point O from the tress is 20m and 60m.

Height = 34.6 m and the distance of point O from the tress is 30m and 30m.

Height = 34.6 m and the distance of point O from the tress is 20m and 50m.

answer is A.

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Detailed Solution

Given that, the two palm trees are of equal height and stand opposite one other on opposite sides of the 80-meter-wide river.
The angles of elevation of the tops of the trees are measured from a point O on the river between them are

60 °

and

30 °

respectively.
Question Image

Let BC = river, AB = CD = palm tree = h and,
OB = x, then OC = 80 – x.
We can observe that, in

Δ A B O

tan 60 ° = h x ⇒ 3 = h x ⇒ 3 x = h ............. (1)

Δ C D O

tan 30 ° = h 80 − x ⇒ 13 = h 80 − x ............. (2)

Substitute eq (1) in (2).
We get,

⇒ 13 = 3 x 80 − x ⇒ 80 − x = 3 x ⇒ 4 x = 80 ⇒ x = 20

Therefore,

h = 3 x = 34.6 m

Now, let us find the height of the trees.

B O = x = 20 m D O = 80 − x = 80 − 20 = 60 m

Height of the trees = 34.6 m and the distance of point O from the tress is 20m and 60m.
The correct option is (1).

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