Question

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A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 5m. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60° and 30° respectively.

Find the height of the tower and the distance of the point from the tower.

(Take$\tt \sqrt{ 3 }$=1.732)​

Answer 1

Question:-

• A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 5m. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60° and 30° respectively. Find the height of the tower and the distance of the point from the tower.

To Find:-

• Find the height of the tower.

Solution:-

Given ,

Height of the flag is 5 m.

Let the height of the tower be ' x '

Distance from the point of the tower is ' y '

• From ∆ACB

$\sf\longrightarrow { \tan(60) }^{\circ} = \dfrac { 5 + x } { y }$

$\sf\longrightarrow y\sqrt { 3 } = 5 + x$ . . . .( i )

• From ∆DBC

$\sf\longrightarrow { \tan(30) }^{\circ} = \dfrac { x } { y }$

$\sf\longrightarrow y = x \sqrt { 3 }$ . . . . ( ii )

• Equation ( i ) = ( ii )

$\sf\longrightarrow 5 + x = \sqrt { 3 } \times x \sqrt { 3 }$

$\sf\longrightarrow 3x - x = 5$

$\sf\longrightarrow 2x = 5$

$\sf\longrightarrow x = \cancel\dfrac { 5 } { 2 }$

$\sf\longrightarrow x = 2.5$

Hence ,

• Height of the tower is 2.5 m

Answer 2

Answer:

As he covered 15 m to the North, 10 m to the West.

So, now the person is in North-West from the house.

Then turned South covering 5 m and then towards East covering 10 m.

So, he covered the 10 m West distance and now he is in the same direction he started from.

Thus, he is to the north from his house.

Hence, A is correct option.

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