To find the height of a right circular cone when given the lengths of the three sides (15 cm, 17 cm, and 16 cm), we can identify that these represent the radius (r), slant height (l), and height (h) of the cone.
Here, we will assume the following:
- The radius (r) = 15 cm
- The height (h) = 16 cm
- The slant height (l) = 17 cm
We can use the Pythagorean theorem, which states: \[ l^2 = r^2 + h^2 \]
Substituting the values we have: \[ 17^2 = 15^2 + h^2 \] \[ 289 = 225 + h^2 \] \[ h^2 = 289 - 225 \] \[ h^2 = 64 \] \[ h = \sqrt{64} \] \[ h = 8 \text{ cm} \]
So, if we assume that 16 cm was the height in your provided dimensions, then the height of the right circular cone is 16 cm, but if you wanted to find the height using the values of radius and slant height correctly, then the height is actually 8 cm if we take the radius as 15 cm and slant height as 17 cm.
To summarize:
- Assumed radius = 15 cm, height = 16 cm (given).
- Calculated height using Pythagorean theorem gives height = 8 cm.
Please clarify if you need a different interpretation, or further assistance!
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