Find the height $ h $ of a rhombus if side $a = 12$ and angle $\beta = 30^o$.
Answer
$h = 6 \sqrt{ 3 }$
Explanation
STEP 1: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \alpha + \beta = 90^o $$After substituting $ \beta = 30^o $ we have:
$$ \alpha + 30^o = 90^o $$ $$ \alpha = 90^o - 30^o $$ $$ \alpha = 60^o $$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 = 12 $ we have:
$$ \sin( 60^o ) = \dfrac{ h }{ 12 } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ 12 } $$$$ h = \frac{\sqrt{ 3 }}{ 2 } \cdot 12 $$$$ h = 6 \sqrt{ 3 } $$This page was created using
Rhombus Calculator