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1. The vertices of a triangle are A(1,4, 2), B(-2, 1, 2), C(2, 3,-4). Find angles A,B,C​

Answer»

Answer:

A=90,B=54.46,C=34.54

Step-by-step explanation:

the vectors along the sides are

AB=B-A=( -3,-3,0),BC=C-B=(4,2,-6),CA=A-C=(-1,1,6)

the SQUARE of the LENGTH of the sides are then

|AB|^2=9+9+0=18

|BC|^2=16+4+36=56

|CA|^2=1+1+36=38

Notice that|AB|^2+|CA|^2=|BC|^2,so by the he converse of PYTHAGORAS theorem ,there is a right ANGLE at A.

for the angle at B ,we have

cosB=|AB/|BC|=3√2/2√14=3/2√7

B=55.46

andC=90-B=34.54


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