STEP 1: find side $ c $

To find side $ c $ use formula:

$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$

After substituting $\alpha = 60^o$ and $h = 3.8\, \text{cm}$ we have:

$$ \sin( 60^o ) = \dfrac{ 3.8\, \text{cm} }{ c } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ 3.8\, \text{cm} }{ c } $$ $$ c = \dfrac{ 3.8\, \text{cm} }{ \frac{\sqrt{ 3 }}{ 2 } } $$ $$ c = 4.3879\, \text{cm} $$

STEP 2: find side $ x $

To find side $ x $ use Pythagorean Theorem:

$$ h^2 + x^2 = c^2 $$

After substituting $h = 3.8\, \text{cm}$ and $c = 4.3879\, \text{cm}$ we have:

$$ \left( 3.8\, \text{cm} \right)^{2} + x^2 = \left( 4.3879\, \text{cm} \right)^{2} $$ $$ x^2 = \left( 4.3879\, \text{cm} \right)^{2} - \left( 3.8\, \text{cm} \right)^{2} $$ $$ x^2 = 19.2533\, \text{cm}^2 - 14.44\, \text{cm}^2 $$ $$ x^2 = 4.8133\, \text{cm}^2 $$ $$ x = \sqrt{ 4.8133\, \text{cm}^2 } $$$$ x = 2.1939\, \text{cm} $$

STEP 3: find long base $ a $

To find long base $ a $ use formula:

$$ x = \frac{ a - b } { 2 } $$

After substituting $x = 2.1939\, \text{cm}$ and $b = 11.9\, \text{cm}$ we have:

$$ 2.1939\, \text{cm} = \frac{ a - 11.9\, \text{cm} } { 2 } $$ $$ 2.1939\, \text{cm} \cdot 2 = a - 11.9\, \text{cm} $$ $$ a - 11.9\, \text{cm} = 4.3879\, \text{cm} $$ $$ a = 4.3879\, \text{cm} + 11.9\, \text{cm} $$ $$ a = 16.2879\, \text{cm} $$

Trapezoid Calculator