To apply the Pythagorean theorem to determine the height \( h \) of a square pyramid, we first need to understand the components involved.
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Identify the components:
- Let \( a \) be the length of a side of the base of the pyramid.
- The height \( h \) is the vertical distance from the apex of the pyramid to the center of the base.
- The slant height \( l \) is the distance from the apex down to the midpoint of one of the edges of the base.
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Use the Pythagorean theorem: The relationship can be expressed using: \[ l^2 = h^2 + \left(\frac{a}{2}\right)^2 \] Where:
- \( l \) is the slant height,
- \( h \) is the height from the apex to the base,
- \( \frac{a}{2} \) is half the side length of the base.
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Rearranging for height \( h \): From the equation above, we can rearrange to solve for \( h \): \[ h^2 = l^2 - \left(\frac{a}{2}\right)^2 \] \[ h = \sqrt{l^2 - \left(\frac{a}{2}\right)^2} \]
Example Calculation
If you provide specific values for \( a \) (the side length of the base) and \( l \) (the slant height), I can calculate the height \( h \) for you.
Final Steps
- Plug in the values of \( a \) and \( l \).
- Calculate the value of \( h \).
- Round \( h \) to the nearest tenth.
Please provide the values for \( a \) and \( l \) so that I can perform the calculations.