Find the diagonal $ d_1 $ of a rhombus if side $a = 12$ and angle $\alpha = 120^o$.
Answer
Problem has no solutions.
Explanation
To find height $ h $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $ \alpha = 120^o $ and $ a = 12 $ we have:
$$ \sin( 120^o ) = \dfrac{ h }{ 12 } $$ $$ - \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ 12 } $$$$ h = - \frac{\sqrt{ 3 }}{ 2 } \cdot 12 $$$$ h = -6 \sqrt{ 3 } $$The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.
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