Question
Find the angle $ \beta $ of a rhombus if diagonal $d_1 = 249.7\, \text{cm}$ and diagonal $d_2 = 251.2\, \text{cm}$.
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 $d_2 = 251.2\, \text{cm}$ and $d_1 = 249.7\, \text{cm}$ we have:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 251.2\, \text{cm} }{ 249.7\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = 1.006 $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( 1.006 \right) $$$ \arcsin(1.006) $ is not defined $ \Longrightarrow $ The problem has no solution.
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