Find the incircle radius $ r $ of a rhombus if side $a = 8$ and angle $\alpha = 45^o$.
Answer
$r = 2 \sqrt{ 2 }$
Explanation
STEP 1: find height $ h $
To find height $ h $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$After substituting $ \alpha = 45^o $ and $ a = 8 $ we have:
$$ \sin( 45^o ) = \dfrac{ h }{ 8 } $$ $$ \frac{\sqrt{ 2 }}{ 2 } = \dfrac{ h }{ 8 } $$$$ h = \frac{\sqrt{ 2 }}{ 2 } \cdot 8 $$$$ h = 4 \sqrt{ 2 } $$STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ h = 2 \cdot r $$After substituting $ h = 4 \sqrt{ 2 } $ we have:
$$ 4 \sqrt{ 2 } = 2 \cdot r $$ $$ r = \dfrac{ 4 \sqrt{ 2 } }{ 2 } $$ $$ r = 2 \sqrt{ 2 } $$This page was created using
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