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Type: Multiple-Choice
Category: Nonlinear Equations and Functions
Level: Grade 11
Standards: HSG-GPE.A.1
Author: nsharp1
Created: 2 years ago

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Nonlinear Equations and Functions Question

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

Now that we have the lengths of the legs of the triangle, what theorem, property, or formula correctly relates them and why is it used?
  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.
  2. 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.
  3. 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.
  4. 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.
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