Find the diagonal $ d_1 $ of a rhombus if diagonal $d_2 = \frac{ 9 }{ 2 }$ and angle $\alpha = 45^o$.
Answer
$d_1 = 11.7591$
Explanation
To find diagonal $ d1 $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$After substituting $ \alpha = \frac{ 45 }{ 2 }^o $ and $ d_2 = \frac{ 9 }{ 2 } $ we have:
$$ \sin \left( \frac{ 45^o }{ 2 } \right) = \dfrac{ d_2 }{ } $$ $$ \sin( \frac{ 45 }{ 2 }^o ) = \dfrac{ \frac{ 9 }{ 2 } }{ d_1 } $$ $$ 0.3827 = \dfrac{ \frac{ 9 }{ 2 } }{ d_1 } $$ $$ d_1 = \dfrac{ \frac{ 9 }{ 2 } }{ 0.3827 } $$ $$ d_1 = 11.7591 $$This page was created using
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