Question

the distance between two poles of equal height is 200 m from a point situated on the line segment joining their bases the angle of elevation of their tops are found to be 60° and 30° find the height of the pole (√3=1.73)​

Answer 1

Answer:

86.70 ( approx )

Step-by-step explanation:

Follow the steps as in the photo

Answer 2

Given:

Distance between two poles=200m

Angles of elevation=60° and 30°

To find:

The height of the pole

Solution:

The height of the pole is 86.5m.

We can find the height by taking the given steps-

We know that the height of both the poles is equal.

Let us assume that the height of each pole is H.

Now, from a point on the line segment joining the bases of poles, the angle of elevation to the top of each pole is 60° and 30°.

Let the distance between one of the poles and this point is D.

So, the distance between this point and the other pole=(200-D)

In the two triangles formed, we will calculate the height of the poles by using trigonometry.

Since tan theta=perpendicular/base, we will find the height of the poles using it.

Tan 60°=H/D

Tan 60°=$\sqrt{3}$

$\sqrt{3}$=H/D

D=H/$\sqrt{3}$

Similarly, tan 30°=H/(200-D)

Tan 30°=1/$\sqrt{3}$

1/$\sqrt{3}$=H/(200-D)

(200-D)=$\sqrt{3}$H

On substituting the value of D, we get

200-H/$\sqrt{3}$=$\sqrt{3}$H

200$\sqrt{3}$-H=$\sqrt{3}$H×$\sqrt{3}$

200$\sqrt{3}$-H=3H

200$\sqrt{3}$=3H+H

200$\sqrt{3}$=4H

50$\sqrt{3}$=H

Now, √3=1.73

So, the height of the pole, H=50×1.73

H=86.5m

Therefore, the height of the pole is 86.5m.