Question
Find the diagonal $ d_1 $ of a rhombus if side $a = 45\, \text{cm}$ and height $h = 45\, \text{cm}$.
Answer
Problem has no solutions.
Explanation
To find angle $ \alpha $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $h = 45\, \text{cm}$ and $a = 45\, \text{cm}$ we have:
$$ \sin \left( \alpha \right) = \dfrac{ 45\, \text{cm} }{ 45\, \text{cm} } $$ $$ \sin \left( \alpha \right) = 1 $$ $$ \alpha = \arcsin\left( 1 \right) $$ $$ \alpha = 90^o $$Angle $ $ \alpha $ $ has to be lesser than 90 degrees $ \Longrightarrow $ The problem has no solution.
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