Find the diagonal $ d_1 $ of a rhombus if side $a = \frac{ 31 }{ 5 }$ 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 = \frac{ 31 }{ 5 } $ we have:
$$ \sin( 120^o ) = \dfrac{ h }{ \frac{ 31 }{ 5 } } $$ $$ - \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ \frac{ 31 }{ 5 } } $$$$ h = - \frac{\sqrt{ 3 }}{ 2 } \cdot \frac{ 31 }{ 5 } $$$$ h = -31 \frac{\sqrt{ 3 }}{ 10 } $$The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.
This page was created using
Rhombus Calculator