Find the height $ h $ of a rhombus if side $a = 10$ and angle $\beta = 60^o$.
Answer
$h = 5$
Explanation
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:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $ \alpha = 30^o $ and $ a = 10 $ we have:
$$ \sin( 30^o ) = \dfrac{ h }{ 10 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ h }{ 10 } $$$$ h = \frac{ 1 }{ 2 } \cdot 10 $$$$ h = 5 $$This page was created using
Rhombus Calculator