Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Deriving the laws of sines and cosines
Derive sine and cosine laws and justify their applicability
Problem types
- Derive and choose a triangle law
Builds on
- Area from two sides and the included angle
- The Pythagorean theorem
- Congruence criteria for triangles · Useful idea
The measurements that determine a triangle by congruence criteria are the measurements the laws of sines and cosines can solve for.
- Proofs about triangles · Useful idea
The altitude and congruence reasoning in triangle proofs is used to derive the laws of sines and cosines.
Leads to
- The laws of sines and cosines · See it applied
The altitude derivation of the laws of sines and cosines shows which measurements each law needs. Solving an oblique triangle applies the matching law to those measurements.
- Polar and Cartesian coordinates · See it applied
The distance between two points given in polar coordinates is found with the law of cosines.
Related skills
- Vectors and their components · Related idea
The law of cosines is the source of the dot product formula for the angle between two vectors.
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