Question
Find the diagonal $ d_2 $ of a rhombus if diagonal $d_1 = 12\, \text{cm}$ and angle $\alpha = 30^o$.
Answer
$3.1058\, \text{cm}$
Explanation
To find diagonal $ d2 $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$After substituting $\alpha = 30^o$ and $d_1 = 12\, \text{cm}$ we have:
$$ \sin \left( \frac{ 30^o }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$ $$ \sin( 15^o ) = \dfrac{ d_2 }{ 12 } $$ $$ 0.2588 = \dfrac{ d_2 }{ 12 } $$$$ d_2 = 0.2588 \cdot 12 $$$$ d_2 = 3.1058 $$This page was created using
Rhombus Calculator