Question
Find the diagonal $ d_1 $ of a rhombus if side $a = 6.2\, \text{cm}$ 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 $a = 6.2\, \text{cm}$ we have:
$$ \sin( 120^o ) = \dfrac{ h }{ 6.2 } $$ $$ - \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ 6.2 } $$$$ h = - \frac{\sqrt{ 3 }}{ 2 } \cdot 6.2 $$$$ h = -5.3694 $$The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.
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