Find the side $ a $ of a pyramid if slant height $s = 51.85$ and lateral edge $e = 57.5$.
Answer
$a = 49.7123$
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$After substituting $ s = 51.85 $ and $ e = 57.5 $ we have:
$$ 51.85^2 + \frac{ a^2 }{ 4 } = 57.5^2 $$ $$ \frac{ a^2 }{ 4 } = 57.5^2 - 51.85^2 $$ $$ \frac{ a^2 }{ 4 } = 3306.25 - 2688.4225 $$ $$ a^2 = 617.8275 \cdot 4 $$ $$ a^2 = 2471.31 $$ $$ a = \sqrt{ 2471.31 } $$$$ a = 49.7123 $$This page was created using
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