Question

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

Answer 1

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

Answer 2

how?

Answer 3

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

Answer 4

o ok yes I thought you wanted it on here

Answer 5

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

Answer 6

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.

Answer 7

20m

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

yes

Answer 12

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.

Answer 13

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.

Answer 14

kind of

Answer 15

Are we unclear about something?

Answer 16

no

Answer 17

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.

Answer 18

Do you know about the Pythagorean Theorem?

Answer 19

ok yea I get that and not really sorry

Answer 20

It's fine. The Pythagorean Theorum says that:

Triangle: Base ^2 + Height ^2 = Hypotenuse ^2

Answer 21

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

Answer 22

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

Answer 23

So if we evaluate:

144 + H^2 = 1024

Answer 24

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

Answer 25

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

Answer 26

Oh, it's alright.