Find the height $ h $ of a pyramid if slant height $s = 36$ and base radius $r = 60$.
Answer
Problem has no solutions.
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ a }{ 2 } $$After substituting $ r = 60 $ we have:
$$ 60 = \dfrac{ a }{ 2 } $$ $$ a = 60 \cdot 2 $$ $$ a = 120 $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$After substituting $ a = 120 $ and $ s = 36 $ we have:
$$ h ^ {\,2} + \frac{ 120^2 }{ 4 } = 36^2 $$ $$ h ^ {\,2} + \frac{ 14400 }{ 4 } = 36^2 $$ $$ h ^ {\,2} + 3600 = 36^2 $$ $$ h ^ {\,2} = 1296 - 3600 $$ $$ h ^ {\,2} = -2304 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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