A rope 32 m long is attached to the top of a flagpole. The rope reaches a place on the ground 12 m from the base of the pole. How many meters high is the flagpole? If necessary, round your answer to the nearest tenth.
A) 34.2
B) 54.0
C) 20.0
D) 29.7

- anonymous

- katieb

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- anonymous

Hello. Can you draw a simple picture of the problem?

- anonymous

how?

- anonymous

Just so you can visualize it, draw a picture of a flagpole on flat ground.

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## More answers

- anonymous

o ok yes I thought you wanted it on here

- anonymous

Haha, sorry. I just meant on some scratch paper somewhere.

- anonymous

So after you have a flagpole, draw the 32m long rope (and label it 32m) from the top of the flagpole to the ground. The rope should reach 12 meters away from the bottom of the flagpole.

- anonymous

20m

- anonymous

"The rope reaches a place on the ground 12 m from the base of the pole" 12 meters is what I understood.

- anonymous

Regardless.
So now you have a picture of a flagpole with rope going diagonally to the ground.

- anonymous

This picture looks an awful lot like a triangle, can we agree?

- anonymous

yes

- anonymous

Great, do you know the parts of your triangles? Right now the rope is the hypotenuse and you should have it labeled 32 meters. From the flagpole to the point where the rope reaches the ground is 12 meters, and you should have it labeled accordingly.

- anonymous

The flagpole coming out of the ground makes a 90 degree angle, that is, the flagpole is perpendicular to the ground. This triangle is a right triangle.

- anonymous

kind of

- anonymous

Are we unclear about something?

- anonymous

no

- anonymous

Oh ok. So we do have a right triangle with the longest side, the hypotenuse being 32 meters. The base of the triangle is 12 meters, from the bottom of the flagpole to the rope.

- anonymous

Do you know about the Pythagorean Theorem?

- anonymous

ok yea I get that and not really sorry

- anonymous

It's fine. The Pythagorean Theorum says that:
Triangle: Base ^2 + Height ^2 = Hypotenuse ^2

- anonymous

ok so 32^2 + 12^2 is the answer?

- anonymous

Not quite. So here we have the hypotenuse = 32m and we have the base = 12m.
So if we just plug that into our equation:
12^2 + Height^2 (We are missing this variable) = 32^2

- anonymous

So if we evaluate:
144 + H^2 = 1024

- anonymous

Can you isolate and solve for H from here? H=Height of the flagpole.

- anonymous

I am sry I will just get help from my teacher I am just not getting it :(

- anonymous

Oh, it's alright.

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