Calculate 82578

The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A.

Correct answer:

c =  5.1962
b =  4.2426
α =  24.8763 °

Step-by-step explanation:

A=(1,2,3) B=(0,1,2) C=(2,1,1)  c=(AxBx)2+(AyBy)2+(AzBz)2=(10)2+(21)2+((3)2)2=3 3=5.1962
b=(AxCx)2+(AyCy)2+(AzCz)2=(12)2+(21)2+((3)1)2=3 2=4.2426
a=(BxCx)2+(ByCy)2+(BzCz)2=(02)2+(11)2+(21)2=52.2361  a2 = b2+c22 b c cos α  α1=arccos(2 b cb2+c2a2)=arccos(2 4.2426 5.19624.24262+5.196222.23612)0.4342 rad  α=α1  °=α1 π180   °=0.4342 π180   °=24.876  °=24.8763=24°5235"

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