Find the angle $ \alpha $ of a rhombus if diagonal $d_1 = \frac{ 9961 }{ 100 }$ and diagonal $d_2 = \frac{ 499 }{ 5 }$.
Answer
Problem has no solutions.
Explanation
To find angle $ \alpha $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$After substituting $ d_2 = \frac{ 499 }{ 5 } $ and $ d_1 = \frac{ 9961 }{ 100 } $ we have:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ \frac{ 499 }{ 5 } }{ \frac{ 9961 }{ 100 } } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 9980 }{ 9961 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 9980 }{ 9961 } \right) $$$ \arcsin(1.002) $ is not defined $ \Longrightarrow $ The problem has no solution.
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