Question

Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet wide. From a point between them on the road, the angles of elevation of the top of the poles are 60 degres and 30 degrees respectively. Find the height of the poles and the distances of the point from the poles​

Answer 1

Answer:

hopefully it should help you

Answer 2

The height of each pole is 51.96 feet and the distance of the second pole from the point is 90 feet.

Step-by-step explanation:

See the attached diagram.

Let, E is the point on the road which is 120 feet wide and the angle of elevation from E to B (top of one pole) is 30° and the elevation from E to D (Top of another pole) is 60°.

Let the height of each pole is H feet.

Then, from right triangle Δ ABE, $\tan 30^{\circ} = \frac{H}{x}$

⇒ H = x tan 30° .......... (1)

Similarly, from right triangle Δ CED, H = (120 - x) tan 60°.

So, we can write, 0.577x = 207.85 - 1.732x

⇒ x = 90 feet.

Hence, from equation (1) we get, H = x tan 30 = 51.96 feet.

Therefore, the height of each pole is 51.96 feet and the distance of the second pole from the point is 90 feet. (Answer)