Find the diagonal $ d_1 $ of a rhombus if diagonal $d_2 = 13542$ and incircle radius $r = 12742$.
Answer
Problem has no solutions.
Explanation
STEP 1: find height $ h $
To find height $ h $ use formula:
$$ h = 2 \cdot r $$After substituting $ r = 12742 $ we have:
$$ h = 2 \cdot 12742 $$ $$ h = 25484 $$STEP 2: find angle $ \beta $
To find angle $ \beta $ use formula:
$$ \sin \left( \frac{ \beta }{ 2 } \right) = \dfrac{ h }{ d_2 } $$After substituting $ h = 25484 $ and $ d_2 = 13542 $ we have:
$$ \sin \left( \frac{ \beta }{ 2 } \right) = \dfrac{ 25484 }{ 13542 } $$ $$ \sin \left( \frac{ \beta }{ 2 } \right) = \frac{ 12742 }{ 6771 } $$ $$ \frac{ \beta }{ 2 } = \arcsin\left( \frac{ 12742 }{ 6771 } \right) $$$ \arcsin(1.882) $ is not defined $ \Longrightarrow $ The problem has no solution.
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