Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 months ago

# Similar Triangles Help?

A string 50 metres long is pegged to the ground and tied to the top of a flagpole. It just touches the head of John. who is 5 metres away from the point where the string is held to the ground. If John is 1.5 metres tall, find the height, h, the flagpole.

I don’t know how to solve this

Relevance

Refer to the picture below.

Using similar triangles we have:

f/1.5 = (a + b)/a

Now, a² = 5² + 1.5² => 27.25

i.e. a = √27.25

Hence, f/1.5 = 50/√27.25

so, f = (50 x 1.5)/√27.25 => 14.37 metres

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• Let h be the heigth of the pole, then

h/50=1.5/sqr(5^2+1.5^2)

=>

h=50*1.5/sqr(27.25)

=>

h=14.36739428~14.37 m

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• Assuming the string is infinitely thin and perfectly straight, the flagpole is infinitely thin and perfectly vertical, the ground is perfectly flat, and John is infinitely thin and perfectly vertical:

1.5*50/sqrt(1.5^2 + 5^2)

= 75/sqrt(2.25 + 25)

= 75/sqrt(27.25)

= 150/sqrt(109)

=~ 14.367394278317270889574890856717

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• Let the peg where the string starts be point A, John's feet point B, John's head point C, flagpole base point D, flagpole top point E.

Assume John and the flag pole each form right angles to the ground, which is assumed to be level.

given AE = 50

BC = 1.5

AB = 5

find DE

AC = √(5^2 + 1.5^2) = √27.25 = 5.220

DE:BC = AE:AC (similar triangles)

x/1.5 = 50/5.22

x = 14.367 m

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• The angle of observation works out as 16.69924423 degrees gleaned from the information about John and so 50 times sine(16.69924423) = 14.3679427 meters or about 14.37 meters which is the height of the flagpole.

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• As always there's ambiguity. I'll assume John's feet are 5 m from where the string is held to the ground.

So you definitely drew this

Length of string from ground to John's head = sqrt(5^2 + 1.5^2) m = 5.22 m

If 5.22 m along the rope from the bottom means 1.5 m height, then 50 ft means 1.5 m * 50/5.22 = 14.4 m height.

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• OK .. this is HOW TO DO IT

You have 2 right angled triangles .. and the string is the hypotenuse.

One triangle is formed by the flagpole, the string, and the ground .. A

One triangle is formed by John, the string, and the ground .. B

Triangle A .. we only know the hypotenuse .. 50 meters

Triangle B .. we don't know the hypotenuse but we do know the other 2 sides .. 5 and 1.5 meters.

So work out the hypotenuse of triangle B using ''the square of the hypotenuse is equal to the sum of the squares of the other two sides''

and then work out what what the proportion of the hypotenuse of B is to A

and that will be the same as the proportion of John's height to the flagpole's height.

• Thank you very much! I didn’t realize that lol.

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