Question

There are two poles,one on each side of the road .the higher pole, the angle of depression of top and bottom of the shorter pole is 30 and 60 degree respectively.find the height of the shorter pole ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Complete Question:

There are two poles, one on each side of the road. The height of the higher pole is 60. From the top of the higher pole, the angle of depression of the top and bottom of the shorter pole is 30 and 60 degrees respectively. Find the height of the shorter pole ​

Answer:

The height of the shorter pole is 40 m.

Step-by-step explanation:

Assumption,

Let the height of the shorter pole be 'h'.

Let the longer pole be AB and the point B on the ground.

Let the shorter pole be CD and the point D on the ground.

Let E is the perpendicular drawn from point C onto the pole AB.

Given,

The angle of depression from point A to point C is 30°.

The angle of depression from point A to point D is 60°.

The height of the longer pole AB = 60.

To find,

The height of the shorter pole (h).

Calculation,

The angle ∠ACE = 30° (As the angle of depression 30° and the angle ACE are alternate angles)

the angle ∠ADB = 60° (Since the angle of depression 60° and ∠ADB are alternate angles).

Now,

tan(30°) = AE/EC...(1)

tan(60°) = AB/EC

⇒ √3 = h/EC

⇒ EC = h/√3 = 60/√3...(2)

Substituting equation (2) in (1)

1/√3 = AE/(60/√3)

⇒ AE = 20m

Hence, the height of the shorter pole is AB - AE = 60 - 20

Therefore, the height of the shorter pole is 40 m

#SPJ2