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?
Made a diagram showing a cross-section of the tent
by ratios
height/ 176 = 112/64
height = 176(112/64)
= ....
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
To calculate the height of the teepee, we can consider it as a right circular cone. Let's call the height of the teepee "h."
We have the following information:
- The girl's height is 112 cm.
- When the girl stands inside the teepee and touches the side, her feet are 64 cm from the edge.
- The diameter of the teepee is 352 cm.
To find the height of the teepee, we can break down the problem into two parts:
1. Calculate the height of the cone by considering the girl's height and her distance from the edge of the teepee.
2. Adjust the calculated cone height to match the actual height of the teepee.
Step 1: Calculate the height of the cone
The distance between the edge of the teepee and the center can be found by subtracting half of the diameter from the distance the girl stands from the edge:
Distance to the cone's center = 352 cm / 2 - 64 cm = 120 cm.
Using the Pythagorean theorem, we can calculate the height of the cone, which is the distance between the cone's center and the top:
h_cone = √(height of the girl)^2 - (distance to cone's center)^2
h_cone = √112^2 - 120^2
h_cone = √12544 - 14400
h_cone = √-184
h_cone ≈ 0 (ignoring the negative value)
Step 2: Adjust the cone height to match the actual height of the teepee
To determine the actual height of the teepee, we need to consider that the cone fits snugly inside the teepee and that there may be some additional height above the cone. This will depend on the shape and design of the teepee.
Without any specific information about the additional height, it is difficult to provide a precise answer. However, based on the given information, we can conclude that the height of the teepee is at least the height of the cone (which is approximately 0 cm).
Therefore, the estimated height of the teepee is 0 cm.