STEP 1: find angle $ \beta $

To find angle $ \beta $ use formula:

$$ \alpha + \beta = 90^o $$

After substituting $ \alpha = 60^o $ we have:

$$ 60^o + \beta = 90^o $$ $$ \beta = 90^o - 60^o $$ $$ \beta = 30^o $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 60^o$ and $a = 1.875\, \text{cm}$ we have:

$$ \sin( 60^o ) = \dfrac{ h }{ 1.875 } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ 1.875 } $$$$ h = \frac{\sqrt{ 3 }}{ 2 } \cdot 1.875 $$$$ h = 1.6238 $$

STEP 3: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

$$ \sin \left( \frac{ \beta }{ 2 } \right) = \dfrac{ h }{ d_2 } $$

After substituting $\beta = 30^o$ and $h = 1.6238\, \text{cm}$ we have:

$$ \sin \left( \frac{ 30^o }{ 2 } \right) = \dfrac{ h }{ d_2 } $$ $$ \sin( 15^o ) = \dfrac{ 1.6238\, \text{cm} }{ d_2 } $$ $$ 0.2588 = \dfrac{ 1.6238\, \text{cm} }{ d_2 } $$ $$ d_2 = \dfrac{ 1.6238\, \text{cm} }{ 0.2588 } $$ $$ d_2 = 6.2739\, \text{cm} $$

Rhombus Calculator