Angle in RT

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

Correct answer:

x =  -90 °

Step-by-step explanation:

a2 + b2 = c2 a2 + (a+d)2 = (a+2d)2 a=1.23 1.232+(1.23+d)2=(1.23+2 d)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=2ab±D=62.46±24.21 d1,2=0.41±0.82 d1=0.41 d2=1.23 d>0 d=d2=(1.23)=100123=1.23 a=1.23 b=a+d=1.23+(1.23)=0 c=a+2 d=1.23+2 (1.23)=100123=1.23 x=π180°arcsin(a/c)=π180°arcsin(1.23/(1.23))=90

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