Find the diagonal $ d_1 $ of a rhombus if incircle radius $r = 21$ and angle $\alpha = 60^o$.
Answer
$d_1 = 84$
Explanation
STEP 1: find height $ h $
To find height $ h $ use formula:
$$ h = 2 \cdot r $$After substituting $ r = 21 $ we have:
$$ h = 2 \cdot 21 $$ $$ h = 42 $$STEP 2: find diagonal $ d1 $
To find diagonal $ d1 $ use formula:
$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ h }{ d_1 } $$After substituting $ \alpha = 30^o $ and $ h = 42 $ we have:
$$ \sin \left( \frac{ 60^o }{ 2 } \right) = \dfrac{ h }{ } $$ $$ \sin( 30^o ) = \dfrac{ 42 }{ d_1 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ 42 }{ d_1 } $$ $$ d_1 = \dfrac{ 42 }{ \frac{ 1 }{ 2 } } $$ $$ d_1 = 84 $$This page was created using
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