Find, correct to the nearest degree, the three angles of the triangle with the g

Question

Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(0,2,2) B(-3,1,3) C(3,1,-2)

Explanation / Answer

PLEASE RATE ME AND AWARD ME KARMA POINTS IF IT IS HELPFUL FOR YOU The line segment AB is parallel to the vector < -2-0,1-3,1-3 > = < -2,-2,-2 > The line segment AC is parallel to the vector < 1-0,5-3,-1-3 > = < 1, 2,-4 > The line segment BC is parallel to the vector < 1-(-2),5-1,-1-1 > = < 3, 4,-2 > We use this formula Angle A is the angle between AB and AC, which is the same angle as the angle between the vectors < -2,-2,-2 > and < 1, 2,-4 > Their dot product is < -2,-2,-2 >@< 1, 2,-4 > = (-2)(1)+(-2)(2)+(-2)(-4) = -2-4+8 = 2 The norm of < -2,-2,-2 > is The norm of < 1,2,-4 > is Substituting in the formula for the cosine, =.1259881577 So A = 82.76217579° or 83° to the nearest degree. -------

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