Find the angle $ \alpha $ of a rhombus if side $a = \frac{ 47 }{ 2 }$ and height $h = 72$.
Answer
Problem has no solutions.
Explanation
To find angle $ \alpha $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $ h = 72 $ and $ a = \frac{ 47 }{ 2 } $ we have:
$$ \sin \left( \alpha \right) = \dfrac{ 72 }{ \frac{ 47 }{ 2 } } $$ $$ \sin \left( \alpha \right) = \frac{ 144 }{ 47 } $$ $$ \alpha = \arcsin\left( \frac{ 144 }{ 47 } \right) $$$ \arcsin(3.064) $ is not defined $ \Longrightarrow $ The problem has no solution.
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