MA19.A2.37 | ALEX

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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

Design by Adaptive Theme

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

Skills

Understanding

Vocabulary

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.