Find the height $ h $ of a rhombus if diagonal $d_1 = 7$ and diagonal $d_2 = \frac{ 9 }{ 2 }$.

$h = 4.5$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$

After substituting $ d_2 = \frac{ 9 }{ 2 } $ and $ d_1 = 7 $ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ \frac{ 9 }{ 2 } }{ 7 } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 9 }{ 14 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 9 }{ 14 } \right) $$ $$ \frac{ \alpha }{ 2 } = 40.0052^o $$$$ \alpha = 40.0052^o \cdot 2 $$$$ \alpha = 80.0104^o $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $ \alpha = 40.0052 $ and $ d_1 = 7 $ we have:

$$ \sin \left( \frac{ 80.0104^o }{ 2 } \right) = \dfrac{ h }{ 7 } $$ $$ \sin( 40.0052 ) = \dfrac{ h }{ 7 } $$ $$ 0.6429 = \dfrac{ h }{ 7 } $$$$ h = 0.6429 \cdot 7 $$$$ h = 4.5 $$

Rhombus Calculator