From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30∘ and 45∘ respectively. Find:i) how far the pole is from the bottom of the tower? ii) the height of the pole. [Use3=1.732]

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From the top of a tower of height 50 m, the angles of depressi

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From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are $3 0^{\circ}$ and $4 5^{\circ}$ respectively. Find:
i) how far the pole is from the bottom of the tower?
ii) the height of the pole. $[U se 3 = 1.732]$

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From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are

3 0^{\circ}

and

4 5^{\circ}

respectively. Find:

i) how far the pole is from the bottom of the tower?

ii) the height of the pole. $[U se 3 = 1.732]$

14 mins ago

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14 mins ago

Text solutionVerified

In this fig, AB is the tower.

CD is the pole.

The distance between the tower and the pole is BC

In right angle triangle ABC, one angle is 45

Hence the other angle is 180-90-45=45

Hence it is a 45 -45- 90 triangle.

BC=AB=50m.

Hence the distance between the tower and the pole is 50m.

Now in rt.angled

△ A E D

E D = BC = 50 m

AED is a 30-60-90 Triangle.

\frac{A E}{E D} = \frac{1}{\sqrt3}

A E = \frac{50}{3}

Hence

BE = A B - A E =

50 - \frac{50}{\sqrt3}

Hence

C D = BE =

height of the pole

= 50 - \frac{50}{\sqrt3}

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Question Text	From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are $3 0^{\circ}$ and $4 5^{\circ}$ respectively. Find: i) how far the pole is from the bottom of the tower? ii) the height of the pole. $[U se 3 = 1.732]$
Answer Type	Text solution:1
Upvotes	150

From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30∘ and 45∘ respectively. Find:i) how far the pole is from the bottom of the tower? ii) the height of the pole. [Use3​=1.732]

Text solutionVerified

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From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are $3 0^{\circ}$ and $4 5^{\circ}$ respectively. Find:
i) how far the pole is from the bottom of the tower?
ii) the height of the pole. $[U se 3 = 1.732]$