Question 193675
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Being a square having 4 equal sides and 4 equal {{{90^o}}} angles. It follows that the diagonal formed a {{{45^o}}} angle = {{{90^o/2=45^o}}}


To prove this using Trigo functions, and based on a 12 inch square tile:
{{{drawing(300,300,-3,3,-3,3,line(-2,2,2,2),line(2,2,2,-2),line(2,-2,-2,-2),line(-2,-2,-2,2),green(line(-2,2,2,-2)),red(locate(-1.8,-1.5,90^o)),red(locate(1.5,1.8,90^o)),red(locate(-1.9,1.5,45^o)),red(locate(-1.5,1.9,45^o)),red(locate(1.2,-1.5,45^o)),red(locate(1.6,-1.1,45^o)),green(locate(0,2.3,12in)),green(locate(2.2,0,12in)),green(locate(0,-2.2,12in)),green(locate(-2.7,0,12in)))}}}


Solving for Diagonal: (Pyth Theorem)
{{{D^2=12^2+12^2=144+144}}}
{{{D=sqrt(288)}}}
{{{D=16.97in}}}

By Trigo function, (Sine-Cosine-Tangent)


{{{Sine(sigma)=opp/hyp=12/16.97}}}
{{{sigma=sin^-1(12/16.97)}}}
{{{red(sigma=45^o)}}}, correct (angle formed by the diagonal and the side)


{{{Cosine(sigma)=adj/hyp=12/16.97}}}
{{{sigma=cos^-1(12/16.97)}}}
{{{red(sigma=45^o)}}}, correct


{{{Tangent(sigma)=opp/adj=12/12}}}
{{{sigma=tan^-1(12/12)=tan^-1(1)}}}
{{{red(sigma=45^o)}}}, correct



Thank you,
Jojo</font>