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Question no -: 38

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Answer 1

$\huge\rm\bold\star\underline\pink{Solution:-}$

Let the height of ballon from ground be 'h' m

Height of ballon from window B = Height of ballon from ground - Height of window B from ground = h - (1.5+3) = h - 4.5 m

Height of ballon from window A = Height of ballon from ground - height of window A from ground = h - 1.5 m

Let horizontal distance between window A and ballon be 'd'

Consider window A ,

Given angle = 45°

$\large\rm{\implies{Tan45°\:=\:\frac{h-1.5}{d}}}$

$\large\rm{\implies{1\:=\:\frac{h-1.5}{d}}}$

$\large\rm{\implies{d\:=\:h-1.5\rightarrow\:eq(1)}}$

Consider Window B ,

Given angle = 30°

$\large\rm{\implies{Tan30°\:=\:\frac{h-4.5}{d}}}$

$\large\rm{\implies{\frac{1}{\sqrt{3}}\:=\:\frac{h-4.5}{d}}}$

$\large\rm{\implies{d\:=\:\sqrt{3}(h-4.5)\rightarrow\:eq(2)}}$

Since in eq(1) and eq(2) LHS is equal so RHS can be equated .

$\large\rm{\implies{(h-1.5)\:=\:\sqrt{3}(h-4.5)}}$

$\large\rm{\implies{(h-1.5)\:=\:\sqrt{3}h-4.5\sqrt{3}}}$

$\large\rm{\implies{\sqrt{3}h-h\:=\:4.5\sqrt{3}-1.5}}$

$\large\rm{\implies{h(\sqrt{3}-1)\:=\:1.5(3\sqrt{3}-1)}}$

$\large\rm{\implies{h\:=\:\frac{1.5(3\sqrt{3}-1)}{(\sqrt{3}-1)}}}$

$\large\rm{\implies{h\:=\:8.59}}$

∴ The height of ballon from ground = 8.59 m

b] If u compare the height between the Ballon and windows window B is more nearer to sanjeev

c] No ,If the ballon moves nearer to the building the angles will not be same .

Answer 2

Hope it helps you........