Question

Plzz solve this fast

Answer 1

Solution :

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Given :

The TV tower on the side of the road,.

A point on the opposite side of the tower shows an angle of elevetion of 60° & 10m away from the point the, angle of elevation decreases to 30°

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To Find :

Height of the tower,..

&

Width of the road,..

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Let the height of the tower be h mts,.

Let the width of the road is x mts,..

Then,


Diagram is as follows,.

A
l\\
l  \ \
l    \   \
I      \    \
I        \      \
l          \        \
l            \         \
l              \           \
l                \            \
l h              \              \
l                   \                \
l                     \                \
L_________\C_______\
Bl-x mts-------l l-10mts----l D

I---------(x + 10) mts --------I

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Given as per diagram,

Buildings aremostly built perpendicular(90°) to the ground,.

Hence,  ∠ABC = 90°

The line of sight is hypotenuse,. (AC & AD)

⇒ ABC & ABD are right angled triangles,.

⇒ We can apply trigonometry,.here,.

⇒ ∠ACB = 60°

⇒ ∠ADB = 30°

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We know that,

In Δ ABC,

tan 60° = √3 = $\frac{AB}{BC} = \sqrt{3}$

⇒ AB = BC√3

⇒ h = x√3    ..........(i)

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In Δ ABD,

⇒ tan 30° = $\frac{1}{ \sqrt{3}} = \frac{AB}{AD}$

⇒ AB√3 = AD

⇒ h√3 = x + 10

⇒ h = $\frac{x + 10}{ \sqrt{3}}$ ....(ii)

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Equating (i) & (ii),

We get,

⇒ $x \sqrt{3} = \frac{x + 10}{ \sqrt{3}}$

⇒ 3x = x + 10

⇒ 3x - x = 10

⇒ 2x = 10

⇒ x = 5 mts,.

Hence, the width of the road is 5 mts,.

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From equation (i),

We get,

⇒ h = x√3

⇒ h = 5√3 mts,.

Hence, the height of the TV tower = 5√3 mts(≈8.66025 mts)

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                                     Hope it Helps!!

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Answer 2

Hope it will help u. . . . .