# Nonlinear Equations and Functions Question

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## Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.1

- The formula for the area of a triangle, [math]A = 1/2 (y-3) * (x-4)[/math], since we know the height and base of the triangle.
- Heron's Formula, [math]A = sqrt(s*(s-a)*(s-b)*(s-c)), " where " s = (2 + (y-4)^2 + (x-3)^2 )/2[/math], because the length of all three sides is known.
- Pythagorean Theorem, [math](x-3)^2 + (y-4)^2 = 4[/math], since the lengths of the three sides of the right triangle are known, and this introduces no extra variables.
- Law of Cosines, [math]|x-3|^2 = 4 + |y-4|^2 - 2*2*|y-4|*cos90°[/math], because the lengths of the three sides of the triangle, and the measure of the right angle, are known, and this introduces no extra variables.