A man stands 9 m away from a flag-pole- He observes that angle of elevation of the top of the pole is 28 - and the angle of depression of the bottom of the pole is 13 - - Calculate the height of the pole-

Let the height of pole and man be l meter and h meter respectively. #10; #10;In Δ ABC #160; tan #10;13^o=h9 ⇒ h=9 tan 13^o ...

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Standard X

Mathematics

Angle of Elevation

A man stands ...

Question

A man stands $9 m$ away from a flag-pole, He observes that angle of elevation of the top of the pole is $28^{\circ}$ and the angle of depression of the bottom of the pole is $13^{\circ} .$ Calculate the height of the pole.

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Solution

Let the height of pole and man be $l m e t e r$ and $h m e t e r$ respectively.

In $Δ A B C$
$t a n 13^{o} = \frac{h}{9} \Rightarrow h = 9 t a n 13^{o}$

In $Δ C D E$
$t a n 28^{o} = \frac{l - h}{9} \Rightarrow l = 9 t a n 28^{o} + 9 t a n 13^{o} = 9 \times 0.531 + 9 \times 0.230 = 6.86 m$

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A man stands 9m away from a flag-pole, He observes that angle of elevation of the top of the pole is 28∘ and the angle of depression of the bottom of the pole is 13∘. Calculate the height of the pole.

Let the height of pole and man be l meter and h meter respectively. In ΔABC tan13o=h9⇒h=9tan 13o In ΔCDE tan28o=l−h9⇒l=9tan28o+9tan13o=9×0.531+9×0.230=6.86m

A man stands $9 m$ away from a flag-pole, He observes that angle of elevation of the top of the pole is $28^{\circ}$ and the angle of depression of the bottom of the pole is $13^{\circ} .$ Calculate the height of the pole.

Let the height of pole and man be $l m e t e r$ and $h m e t e r$ respectively.

In $Δ A B C$
$t a n 13^{o} = \frac{h}{9} \Rightarrow h = 9 t a n 13^{o}$

In $Δ C D E$
$t a n 28^{o} = \frac{l - h}{9} \Rightarrow l = 9 t a n 28^{o} + 9 t a n 13^{o} = 9 \times 0.531 + 9 \times 0.230 = 6.86 m$