Prove $Delta text{ABC}$ is a right triangle?
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Prove $Delta text{ABC}$ is a right triangle if: $$left{begin{matrix} sin^{2},text{A}+ sin^{2},text{B}= sin text{C}\ maxleft { measuredangle text{A}- text{k},measuredangle text{B},,measuredangle text{B}- text{k},measuredangle text{A} right }leqq frac{pi }{2}\ left | text{k} right |leqq 3 end{matrix}right.$$ I have a proof for my problem with $text{k}= 0$ . See here: $lceil$ https://diendantoanhoc.net/topic/185093-measuredangle-textc-pi/#entry716757 $rfloor$ I also have another solution but ugly, I try to use similar method with $left | text{k} right |leqq 3$ but without success !
geometry trigonometry inequality
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