The angle of elevation of the top of a tower from a point on the ground 30∘ after walking 200 m towards the tower the angle of elevation becomes 60∘. The height of the tower is

Let h be the height of the towerIn ΔABCtan600=BCAB=>3=xh=>x=3h .......(i)In ΔABDtan300=BDAB=>31=x+200h=>x+200=3h=>x=3h−200 .......(ii)From (i) and (ii) we get,3h=3h−200=>h=3h−2003=>2h=2003h=>1003m=>h=100x1.732=>h=173.2 metre∴ Height of tower =173.2 m.

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The angle of elevation of the top of a tower from a point on t

Question

The angle of elevation of the top of a tower from a point on the ground $3 0^{\circ}$ after walking $200$ m towards the tower the angle of elevation becomes $6 0^{\circ}$ . The height of the tower is

1003

2003

100

200

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The angle of elevation of the top of a tower from a point on the ground

3 0^{\circ}

after walking

200

m towards the tower the angle of elevation becomes

6 0^{\circ}

. The height of the tower is

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Let

h

be the height of the tower

Δ A BC

t an 6 0^{0} = \frac{A B}{BC}

=> 3 = \frac{h}{x}

=> x = \frac{h}{3}

.......(i)

Δ A B D

t an 3 0^{0} = \frac{A B}{B D}

=> \frac{1}{3} = \frac{h}{x + 200}

=> x + 200 = 3 h

=> x = 3 h - 200

.......(ii)

From (i) and (ii) we get,

\frac{h}{3} = 3 h - 200

=> h = 3 h - 2003

=> 2 h = 2003

h => 1003

=> h = 100 x 1.732

=> h = 173.2

metre

∴ Height of tower =

173.2

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Question Text	The angle of elevation of the top of a tower from a point on the ground $3 0^{\circ}$ after walking $200$ m towards the tower the angle of elevation becomes $6 0^{\circ}$ . The height of the tower is
Answer Type	Text solution:1
Upvotes	150

The angle of elevation of the top of a tower from a point on the ground 30∘ after walking 200 m towards the tower the angle of elevation becomes 60∘. The height of the tower is

Text solutionVerified

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The angle of elevation of the top of a tower from a point on the ground $3 0^{\circ}$ after walking $200$ m towards the tower the angle of elevation becomes $6 0^{\circ}$ . The height of the tower is