Angle in RT

Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.

Correct result:

x =  90 °

Solution:

a2+b2=c2 a2+(a+d)2=(a+2d)2 a=1.23 1.232+(1.23+d)2=(1.23+2d)2  1.232+(1.23+d)2=(1.23+2 d)2 3d22.46d+1.513=0 3d2+2.46d1.513=0  a=3;b=2.46;c=1.513 D=b24ac=2.46243(1.513)=24.2064 D>0  d1,2=b±D2a=2.46±24.216 d1,2=0.41±0.82 d1=0.41 d2=1.23   Factored form of the equation:  3(d0.41)(d+1.23)=0 d>0 d=d2 a=1.23 b=a+d=1.23+d=123100=1.23 c=a+2 d=1.23+2 d=123100=1.23 x=180πarcsin(a/c)=180πarcsin(1.23/1.23)=90

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