MA19.A2.37

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.37

Derive and apply the formula $A = \frac{1}{2} \cdot ab \cdot \sin(C)$ for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side, extending the domain of sine to include right and obtuse angles.

Unpacked Content

Knowledge

Students know:
  • The auxiliary line drawn from the vertex perpendicular to the opposite side forms an altitude of the triangle.
  • The formula for the area of a triangle (A = 1/2 bh).
  • Properties of the sine ratio.

Skills

Students are able to:
  • Properly label a triangle according to convention.
  • Perform algebraic manipulations.

Understanding

Students understand that:
  • Given the lengths of the sides and included angle of any triangle the area can be determined.
  • There is more than one formula to find the area of a triangle.

Vocabulary

  • Auxiliary line
  • Vertex
  • Perpendicular

Aligned Learning Resources

Triangle Area: No Height?--Use the Sine
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