A tower and the pole stand vertically on the same level of ground . it is observed that the angles of depression of top and the foot of the pole from the top of the tower of height 60 m is 30degree respective find the height of the tower.
Answers
Answer:
A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is 60^o .
Correct Question:
A tower and a pole stand vertically on the same level of ground. It is observed that the angles of depression of top and the foot of the pole from the top of the tower of height 60 m is 30° and 60° respectively. Find the height of the pole. [ As the height of the tower is already given we need to find the height of pole not the height of tower ].
Given:
✰ A tower and a pole stand vertically on the same level of ground.
✰ Height of the tower = 60 m
✰ It is observed that the angles of depression of top and the foot of the pole from the top of the tower of height is 30° and 60° respectively.
To find:
✠ The height of the pole.
Solution:
Let AB be the height of the tower and CD be the height of the pole.
As, we are provided with AB = 60 m
⤳ Angle of elevation = Angle of depression
⤳ tan 60° = AB/BD
⤳ √3 = 60/BD
⤳ √3 × BD = 60
⤳ BD = 60/√3
Rationalize
⤳ BD = (60 × √3)/(√3 × √3)
⤳ BD = (60√3)/((√3)²)
⤳ BD = (60√3)/3
⤳ BD = 20√3 m
Then,
⤳ tan 30° = AE/EC
⤳ 1/√3 = AE/20√3 [ ∵ EC = BD = 20√3 ]
⤳ AE = 20√3/√3
⤳ AE = 20 m
Now, finally find the height of pole i.e, CD
⤳ AE = AB - CD
⤳ 20 = 60 - CD
⤳ CD = 60 - 20
⤳ CD = 40 m
∴ The height of the pole = 40 m
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