Find the side $ a $ of an equilateral triangle if altitude $h = 23$.
Answer
$a = \frac{ 46 \sqrt{ 3}}{ 3 }$
Explanation
To find side $ a $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ h = 23 $ we have:
$$ 23 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 23 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 46 $$ $$ a = \dfrac{ 46 }{ \sqrt{ 3 } } $$ $$ a = \frac{ 46 \sqrt{ 3}}{ 3 } $$This page was created using
Equilateral Triangle Calculator