STEP 1: find side $ a $

To find side $ a $ use formula:

$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $h = 5\, \text{cm}$ we have:

$$ 5\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 5\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 10\, \text{cm} $$ $$ a = \dfrac{ 10\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 10 \sqrt{ 3}}{ 3 }\, \text{cm} $$

STEP 2: find circumradius $ R $

To find circumradius $ R $ use formula:

$$ R = \dfrac{ \sqrt{ 3 } \cdot a }{ 3 } $$

After substituting $a = \dfrac{ 10 \sqrt{ 3}}{ 3 }\, \text{cm}$ we have:

$$ R = \dfrac{ \sqrt{ 3 } \cdot \frac{ 10 \sqrt{ 3}}{ 3 }\, \text{cm} }{ 3 } $$$$ R = \dfrac{ 10\, \text{cm} }{ 3 } $$ $$ R = \frac{ 10 }{ 3 }\, \text{cm} $$

Equilateral Triangle Calculator