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# Understanding this formula: area = 0.5 a * b * sinc watch

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1. I'm assuming this is correct:
C is the angle between the sides a and b
B is the angle between the sides a and c
A is the angle between the sides c and b

Here is the problem: The area of the triangle is 100cm^2
http://imageshack.us/photo/my-images/17/triangle3.jpg/

I have to find angle ABC

formula: Area = 0.5 * a * b * sin(c)
so 100cm^2 = 0.5 * AB * AC * sin(BAC)
so 100cm^2 = 0.5 * 16cm * 16cm * SIN(BAC)
So angle BAC = 51.375

So ABC should be (180-51.375)/2 = 64.1
but the book says ABC = 51.4..
Does the formula not work for an isosceles?
2. (Original post by Bobby132)
I'm assuming this is correct:
C is the angle between the sides a and b
B is the angle between the sides a and c
A is the angle between the sides c and b

Here is the problem: The area of the triangle is 100cm^2
http://imageshack.us/photo/my-images/17/triangle3.jpg/

I have to find angle ABC

formula: Area = 0.5 * a * b * sin(c)
so 100cm^2 = 0.5 * AB * AC * sin(BAC)
so 100cm^2 = 0.5 * 16cm * 16cm * SIN(BAC)
So angle BAC = 51.375

So ABC should be (180-51.375)/2 = 64.1
but the book says ABC = 51.4..
Does the formula not work for an isosceles?
the formula works for all triangles, there could be an error in your book
3. Your triangle is not labelled properly. This is how you should label it.

You can check that the above information agrees.

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