Question
Find the diagonal $ d_2 $ of a rhombus if diagonal $d_1 = 10\, \text{cm}$ and angle $\alpha = 45^o$.
Answer
$3.8268\, \text{cm}$
Explanation
To find diagonal $ d2 $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$After substituting $\alpha = 45^o$ and $d_1 = 10\, \text{cm}$ we have:
$$ \sin \left( \frac{ 45^o }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$ $$ \sin( \frac{ 45 }{ 2 }^o ) = \dfrac{ d_2 }{ 10 } $$ $$ 0.3827 = \dfrac{ d_2 }{ 10 } $$$$ d_2 = 0.3827 \cdot 10 $$$$ d_2 = 3.8268 $$This page was created using
Rhombus Calculator