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I am having difficulty with this problem. Any help would be greatly appreciated.

Consider the triangle A(1, 0, 0), B(0, 2, 0) and C(0, 3, 4).

Find the obtuse angle of the triangle ABC. Find the area of ABC.

The line AB = (-1,2,0).

The line AC = (-1,3,4).

It is known that the magnitude of the cross product is the area of the rectangle between them.

The triangle has one half of this area.

The cross product is (2*4 - 0*3, 0*-1 - -1*4, -1*-3 - -1*2).

Since 2*4 = 8 and 0*3 = 0, the x term is 8.

Since 0*-1 = 0 and --1*4 = 4, they y term is 4.

Since -1*-3 = 3 and --1*2 = 2, the z term is 2.

The length of this is sqrt(8²+4²+2²) = sqrt(64+16+4) = sqrt(84).

Since 84 is a little bigger than 81, which is 9², I would guess than answer to be 9.15.

Doing it in Excel gives the true answer as 84^0.5 = 9.16515139 as the area of the parallelogram.

The area of the triangle is 1/2 of this, which is 4.582575695.

An answer of 4.58 would probably be good enough.

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