Question
Find the angle $ \alpha $ of a rhombus if side $a = 24\, \text{cm}$ and height $h = 27\, \text{cm}$.
Answer
Problem has no solutions.
Explanation
To find angle $ \alpha $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $h = 27\, \text{cm}$ and $a = 24\, \text{cm}$ we have:
$$ \sin \left( \alpha \right) = \dfrac{ 27\, \text{cm} }{ 24\, \text{cm} } $$ $$ \sin \left( \alpha \right) = \frac{ 9 }{ 8 } $$ $$ \alpha = \arcsin\left( \frac{ 9 }{ 8 } \right) $$$ \arcsin(1.125) $ is not defined $ \Longrightarrow $ The problem has no solution.
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