SOLUTION: Can anyone help me with this cone problem? I have no idea where to begin. A girl wants to calculate the height of a tee-pee, she is 112cm tall. When she stands inside with her h

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Question 326249: Can anyone help me with this cone problem? I have no idea where to begin. A girl wants to calculate the height of a tee-pee, she is 112cm tall. When she stands inside with her head touching the side, her feet are 64cm from the edge. The tee-pee is a right circular cone with a diameter of 352cm, what is it's height? Any help would be appreciated!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A girl wants to calculate the height of a tee-pee, she is 112cm tall. When she stands inside with her head touching the side, her feet are 64cm from the edge. The tee-pee is a right circular cone with a diameter of 352cm, what is it's height? Any help would be appreciated!
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Since the diameter of the base = 352 cm, d = 352/pi = 112.05
So radius = 56.025 cm
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Draw a picture of a vertical cross-section of the tee-pee
with a vertical line segment (the girl) 64 cm from one outer edge
and 48.05 cm from the other edge.
----
You should see two overlapping right triangles that are
proportional, with enough
information to solve for the height of the tee-pee.
======================================================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First take half of the diameter to get 176 cm. So the radius is 176 cm.

Now draw the picture to get



Note: the red line represents the girl.


Now to find the height x, notice how the smaller triangle is similar to the larger one. So this means that the corresponding sides form the same ratio. So this means that x%2F176=112%2F64 (ie the ratio of the height to the horizontal distance is the same). Simply solve x%2F176=112%2F64 to find the height 'x'.