The angle of elevation of the top of a chimney is $45^{\circ}$ from a point on the ground at a distance of 200 metres from the base of the chimney. The height of the chimney is

100 \sqrt{2} m

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50 \sqrt{2} m

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200 m

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200 \sqrt{2} m

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Solution

The correct option is C $200 m$
AB = perpendicular = Height of chimney
AC = Hypotenuse
BC = Base = distance between point on ground and base of chimney

$t a n θ = \frac{P e r p e n d i c u l a r}{B a s e} = \frac{A B}{B C}$
$\Rightarrow t a n 45^{\circ} = \frac{A B}{200}$
$\Rightarrow 1 = \frac{A B}{200} (t a n 45^{\circ} = 1)$
$\Rightarrow A B = 200 m$

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The angle of elevation of the top of a chimney is 45∘ from a point on the ground at a distance of 200 metres from the base of the chimney. The height of the chimney is

The correct option is C 200 mAB = perpendicular = Height of chimney AC = Hypotenuse BC = Base = distance between point on ground and base of chimney tan θ=PerpendicularBase=ABBC ⇒tan 45∘=AB200 ⇒1=AB200(tan 45∘=1) ⇒AB=200 m

The angle of elevation of the top of a chimney is $45^{\circ}$ from a point on the ground at a distance of 200 metres from the base of the chimney. The height of the chimney is