#### 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

## UP:MA19.A2.37

### Vocabulary

- Auxiliary line
- Vertex
- Perpendicular

### Knowledge

- 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

- Properly label a triangle according to convention.
- Perform algebraic manipulations.

### Understanding

- 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.