Math, asked by singhsarvjeet1721, 1 year ago

The distance between two vertical pillars is 100 m and height of one of them is double of the other the angle of elevation of the top at the midpoint of the line joining their seats are complementary find their heights

Answers

Answered by sprao534
42
Please see the attachment
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Answered by wifilethbridge
11

Answer:

The height of towers is 35.35 m and 70.7 m

Step-by-step explanation:

Refer the attached figure

The distance between two vertical pillars is 100 m i.e. AB = 100 m

Let the height of one pillar i.e. CB = x

Now we are given that height of one of them is double of the other.

So, The height of other pillar i.e. AD = 2x

Now we are given that the angle of elevation of the top at the midpoint i.e. E of the line joining their seats are complementary

∠CEB = y

So, ∠CEA=90-y

AE = EB = 50 m

In ΔACE

cot \theta =\frac{AE}{AD}

Cot(90-y) =\frac{50}{2x}

tan y=\frac{50}{2x}  ---1

In ΔECB

tan \theta =\frac{CB}{EB}

tan y =\frac{x}{50}---2

Equate 1 and 2

\frac{x}{50}=\frac{50}{2x}

2x^2=2500

x^2=1250

x=\sqrt{1250}

x=35.35

So, Height of tower CB is 35.35 m

Height of tower AD = 2x= 2(35.35)=70.7m

Hence The height of towers is 35.35 m and 70.7 m

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