Question

A pole of height 14 metre cast a 10 metre long shadow on the ground at the same time a tower cast a 70 metre long shadow on ground find the height of Tower

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Height\:of\:tower=98\:m}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a pole of height 14 metre cast a 10 metre long shadow on the ground at the same time a tower cast a 70 metre long shadow on ground.

• We have to find the height of Tower

$\underline \bold{Given : } \\ \implies Height \: of \: pole = 14 \: m \\ \\ \implies Shadow \: of \: pole = 10 \: m \\ \\ \implies Shadow \: of \: tower = 70 \: m \\ \\ \underline \bold{To \: Find : } \\ \implies Height \: of \: tower = ?$

• According to given question :

$\bold{For \: pole : } \\ \implies tan \: \theta = \frac{p}{b} \\ \\ \implies tan \: \theta = \frac{Height \: of \: pole} {Shadow \: of \: pole} \\ \\ \implies tan \: \theta = \frac{14}{10} \\ \\ \implies tan \: \theta = \frac{7}{5} \\ \\ \bold{For \: tower : } \\ \implies tan \: \theta = \frac{Height \: of \: tower}{Shadow \: of \: tower} \\ \\ \implies \frac{7}{5} = \frac{H}{70} \\ \\ \implies 4 \: H= 490\\ \\ \implies H = \frac{ \cancel{490}}{ \cancel{5 }} \\ \\ \bold{\implies H= 98 \: m}$

Answer 2

AnswEr :

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Height of Tower is 98 metre.

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Explanation :

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As Both the Pole and the Tower are At Same Angle. So Let's Take that Angle as ∅.

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$\Rightarrow\bf{\angle\:Cast\:by\:Pole = \angle\:Cast\:by\:Tower}$

$\Rightarrow\bf{tan \theta=Tan \theta}$

$\Rightarrow\bf{ \dfrac{p}{b}= \dfrac{P}{B}}$

$\Rightarrow\bf{ \dfrac{Height\:of\:Pole}{Shadow\:of\:Pole}= \dfrac{Height\:of\:Tower}{Shadow\:of\:Tower}}$

$\Rightarrow\bf{ \dfrac{14}{10}= \dfrac{P}{70}}$

$\Rightarrow\bf{ P= \dfrac{14\times 70}{10}}$

$\Rightarrow\bf{ P= 14\times 7}$

$\Rightarrow\boxed{\large{\bf{ P= 98m}}}$

⠀

$\large\therefore$ Height of Tower is 98m.