Find the diagonal $ d_1 $ of a rhombus if diagonal $d_2 = 30$ and angle $\alpha = 120^o$.
Answer
$d_1 = 20 \sqrt{ 3 }$
Explanation
To find diagonal $ d1 $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$After substituting $ \alpha = 60^o $ and $ d_2 = 30 $ we have:
$$ \sin \left( \frac{ 120^o }{ 2 } \right) = \dfrac{ d_2 }{ } $$ $$ \sin( 60^o ) = \dfrac{ 30 }{ d_1 } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ 30 }{ d_1 } $$ $$ d_1 = \dfrac{ 30 }{ \frac{\sqrt{ 3 }}{ 2 } } $$ $$ d_1 = 20 \sqrt{ 3 } $$This page was created using
Rhombus Calculator