two vertical poles of different height are standing 25 metre away from each other on the same level ground the angle of evolution of the top of one angle at the photo of the other is 60 degree and the angle of elevation of the top of the Other at the foot of the first is 45 degree find the difference between the height of the poles
Answers
Given :- (From image) .
- AB = Shorter Pole = Let h m.
- EC = Taller Pole = Let H m .
- BC = 25m .
- ∠ACB = 45° .
- ∠EBC = 60° .
To Find :-
- ED = ?
Solution :-
in Right angled ∆ABC , we have,
→ Tan 45° = AB / BC
→ 1 = h / 25
→ h = 25 m .
in Right angled ∆EBC, we have,
→ EC = ED + DC .
→ EC = ED + 25. ( ∵ DC = h } .
→ Tan 60° = EC / CB
→ √3 = (ED + 25) / 25
→ 25√3 = ED + 25
→ 25√3 - 25 = ED
→ ED = 25(√3 - 1)
→ ED = 25(1.732 - 1)
→ ED = 25 * 0.732
→ ED = 18.3 m (Ans.)
Hence, The difference between the height of the poles is 18.3 m.
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