Find the side $ a $ of a rhombus if diagonal $d_1 = 15$ and height $h = 7$.

$a = 8.48$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $ h = 7 $ and $ d_1 = 15 $ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 7 }{ 15 } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 7 }{ 15 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 7 }{ 15 } \right) $$ $$ \frac{ \alpha }{ 2 } = 27.8181^o $$$$ \alpha = 27.8181^o \cdot 2 $$$$ \alpha = 55.6363^o $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $ \alpha = 55.6363^o $ and $ h = 7 $ we have:

$$ \sin( 55.6363^o ) = \dfrac{ 7 }{ a } $$ $$ 0.8255 = \dfrac{ 7 }{ a } $$ $$ a = \dfrac{ 7 }{ 0.8255 } $$ $$ a = 8.48 $$

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