Question
Find the diagonal $ d_1 $ of a rhombus if diagonal $d_2 = 5\, \text{cm}$ and angle $\alpha = 45^o$.
Answer
$13.0656\, \text{cm}$
Explanation
To find diagonal $ d1 $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$After substituting $\alpha = 45^o$ and $d_2 = 5\, \text{cm}$ we have:
$$ \sin \left( \frac{ 45^o }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$ $$ \sin( \frac{ 45 }{ 2 }^o ) = \dfrac{ 5\, \text{cm} }{ d_1 } $$ $$ 0.3827 = \dfrac{ 5\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 5\, \text{cm} }{ 0.3827 } $$ $$ d_1 = 13.0656\, \text{cm} $$This page was created using
Rhombus Calculator