Find the height $ h $ of a rhombus if diagonal $d_1 = 84$ and angle $\beta = 60^o$.

$h = 21.7408$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

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

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

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $ \alpha = 15^o $ and $ d_1 = 84 $ we have:

$$ \sin \left( \frac{ 30^o }{ 2 } \right) = \dfrac{ h }{ 84 } $$ $$ \sin( 15^o ) = \dfrac{ h }{ 84 } $$ $$ 0.2588 = \dfrac{ h }{ 84 } $$$$ h = 0.2588 \cdot 84 $$$$ h = 21.7408 $$

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