MATHS - CLASS X
From a balloon vertically above a straight road, the angle of depression of two cars at an instant are found to be 45° and 60°. If the cars are 100m apart, find the height of the balloon.
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Hello
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Please refer to the attachment for the diagram.
Let , A be the position of the balloon.
C and D are the positions of the two cars respectively.
So, CD = 100 m
Let , BC = x m
AB = ?
Then,
In ∆ABC,
AB/BC = tan60°
AB/x = √3
AB = √3x .......(i)
Again, In ∆ABD,
AB/BD = tan45°
AB/(x + 100) = 1
=> AB = x + 100 ........(ii)
=> √3x - x = 100 [From (i)]
=> x(√3 - 1 ) = 100
=> x = 100/(√3 - 1)
Now, Rationalising ,
So, x = 136.6 m
Then,
AB = x + 100 [From (ii)]
= (136.6 + 100) m
= 236.6 m
Therefore,
Height of the balloon = 236.6 m
#Redesign
#Rebuild
#Reclaim
ArchitectSethRollins
----------
Please refer to the attachment for the diagram.
Let , A be the position of the balloon.
C and D are the positions of the two cars respectively.
So, CD = 100 m
Let , BC = x m
AB = ?
Then,
In ∆ABC,
AB/BC = tan60°
AB/x = √3
AB = √3x .......(i)
Again, In ∆ABD,
AB/BD = tan45°
AB/(x + 100) = 1
=> AB = x + 100 ........(ii)
=> √3x - x = 100 [From (i)]
=> x(√3 - 1 ) = 100
=> x = 100/(√3 - 1)
Now, Rationalising ,
So, x = 136.6 m
Then,
AB = x + 100 [From (ii)]
= (136.6 + 100) m
= 236.6 m
Therefore,
Height of the balloon = 236.6 m
#Redesign
#Rebuild
#Reclaim
ArchitectSethRollins
Attachments:
Mylo2145:
Awesome! U cleared my doubts! Thanku!
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