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A pole of height 60m has a shadow of length 20√3m at a particular instant of time. The angle of elevation of the sun at this point of time
- a)30°
- b)45°
- c)60°
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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A pole of height 60m has a shadow of length 20√3m at a particula...
Given,
[•] Height of the pole (AB) = 60m.
[•] Pole having shadow of length (BC) = 20√3m.
[•] Angle of elevation of the Sun (AC) = ?
Solution:-
[•] Let the angle of elevation be taken as "θ".
[•] Let the height of the pole (AB) be taken as "Perpendicular" or "Opposite side".
[•] Let the shadow of pole (BC) be taken as "Base" or "Adjacent".
We can find the Angle of elevation of the Sun by using Tan θ. So, Let us see..
Tan θ = Opposite side / Adjacent = AB/BC.
Tan θ = 60/20√3.
Tan θ = 3/√3.
Rationalize the denominator term i.e. √3.
=> 3/√3 × √3×√3.
=> 3√3/(√3)².
Square root and Square gets cancel for (√3)². Then, we get 3 in denominator.
=> 3√3/3.
Now the 3 and 3 gets cancel in both numerator and denominator. Then we get √3 as answer.
=> √3.
Now, what is the trignometric ratio of √3 in Tan θ? It is 60 degree.
Hence, Option (c) 60 degree is the correct answer..
[•] Height of the pole (AB) = 60m.
[•] Pole having shadow of length (BC) = 20√3m.
[•] Angle of elevation of the Sun (AC) = ?
Solution:-
[•] Let the angle of elevation be taken as "θ".
[•] Let the height of the pole (AB) be taken as "Perpendicular" or "Opposite side".
[•] Let the shadow of pole (BC) be taken as "Base" or "Adjacent".
We can find the Angle of elevation of the Sun by using Tan θ. So, Let us see..
Tan θ = Opposite side / Adjacent = AB/BC.
Tan θ = 60/20√3.
Tan θ = 3/√3.
Rationalize the denominator term i.e. √3.
=> 3/√3 × √3×√3.
=> 3√3/(√3)².
Square root and Square gets cancel for (√3)². Then, we get 3 in denominator.
=> 3√3/3.
Now the 3 and 3 gets cancel in both numerator and denominator. Then we get √3 as answer.
=> √3.
Now, what is the trignometric ratio of √3 in Tan θ? It is 60 degree.
Hence, Option (c) 60 degree is the correct answer..
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A pole of height 60m has a shadow of length 20√3m at a particular instant of time. The angle of elevation of the sun at this point of timea)30°b)45°c)60°d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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