STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $h = 6.93\, \text{cm}$ and $a = 8\, \text{cm}$ we have:

$$ \sin \left( \alpha \right) = \dfrac{ 6.93\, \text{cm} }{ 8\, \text{cm} } $$ $$ \sin \left( \alpha \right) = 0.8663 $$ $$ \alpha = \arcsin\left( 0.8663 \right) $$ $$ \alpha = 60.0257^o $$

STEP 2: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ h }{ d_1 } $$

After substituting $\alpha = 60.0257^o$ and $h = 6.93\, \text{cm}$ we have:

$$ \sin \left( \frac{ 60.0257^o }{ 2 } \right) = \dfrac{ h }{ d_1 } $$ $$ \sin( 30.0129 ) = \dfrac{ 6.93\, \text{cm} }{ d_1 } $$ $$ 0.5002 = \dfrac{ 6.93\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 6.93\, \text{cm} }{ 0.5002 } $$ $$ d_1 = 13.8546\, \text{cm} $$

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