MA19.A2.38

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

MA19.A2.38
Derive and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. Extend the domain of sine and cosine 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.
Properties of the Sine and Cosine ratios.
Pythagorean Theorem.
Pythagorean Identity.
The Laws of Sines and Cosines can apply to any triangle, right or non-right.
Laws of Sines and Cosines.
Vector quantities can represent lengths of sides and angles in a triangle.
Values of the sin(90 degrees) and cos(90 degrees).

Skills

Students are able to:

Label triangles in context and by convention.
Perform algebraic manipulations.
Find inverse sine and cosine values.

Understanding

Students understand that:

The given information will determine whether it is appropriate to use the Law of Sines or the Law of Cosines.
Proof is necessary to establish that a conjecture about a relationship in mathematics is always true and may provide insight into the mathematics being addressed.
Proven laws allow us to solve problems in contextual situations.

Vocabulary

Law of Sines
Law of Cosines
Resultant Force

COS Examples

Examples: surveying problems, resultant forces

Design by Adaptive Theme