Math, asked by Mylo2145, 1 year ago

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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Answers

Answered by ArchitectSethRollins
24
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 ,

 \frac{100}{( \sqrt{3} - 1) } \times \frac{( \sqrt{3} + 1) }{( \sqrt{3} + 1)} \\ \\ = \frac{100( \sqrt{3} + 1)}{( \sqrt{3}) {}^{2} - (1) {}^{2} } \\ \\ = \frac{100( \sqrt{3} + 1)}{3 - 1} \\ \\ = \frac{100( \sqrt{3} - 1) }{2} \\ \\ = \frac{ \cancel {100} \: \: {}^{50} ( \sqrt{3} + 1) }{ \cancel 2} \\ \\ = 50 (1.732 + 1) \\ \\ = 50 \times 2.732 \\ \\ = 136.6

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!
ArchitectSethRollins: Welcome!
HarishAS: Great answer ji.
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