# geometry

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A girl wants to calculate the height of her family's teepe. She iss 112 cm tall and she finds that when she is inside and stands so that hher head touches the side, her feet are 64 cm from the edge. If the teepe is a right circular cone with a diamter of 352 cm, what is its height?

• geometry -

Made a diagram showing a cross-section of the tent
by ratios

height/ 176 = 112/64
height = 176(112/64)
= ....

• geometry -

The cone base radius is 176 cm.

Based upon similar right triangles,
112/64 = H/176

One of the triangles has the side of the tent for the hypotenuse, the radius for one side and the tent height for the other side. For the second triangle, the girl standing up is the vertical side, and the 64 cm length is the base. All angles are the same.

H = 308 cm

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