Partial derivatives on area of a triangle

analysis multivariable-calculus triangles

Solution 1:

You won't find an expression for $\omega(x,y)$ because it doesn't exist. The angle between two sides is free to vary when only their lengths are specified.

Generally a triangle cannot be specified (up to an isometry) without three parameters (SAS, SSS work, for example).

I hope writing $E = E(x,y,\omega)$ will then make your problem simple.

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