Common Core · High school
HSG-SRT.D.11
High school — Understand and apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles. (+)
High school — Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g. surveying problems, resultant forces).
A note on this mapping: HSG-SRT.D.11 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Geometry. The dot product itself has no Common Core code; this skill is tagged by the resultant-force and velocity standards that do exist.
The 2 skills that cover it
- Law of Sines & CosinesSolve triangles that are not right-angled using the law of sines and the law of cosines.Read the lesson →
- Dot Product & Vector ApplicationsPut vectors to work: the dot product, the angle between two vectors, when they are perpendicular, the projection of one onto another, work done by a force, and the resultant of forces, winds and currents.Read the lesson →
What a student should be able to do
- Choose between the law of sines and the law of cosines.
- Find a missing side or angle in an oblique triangle.
- Find the area of a triangle from two sides and the included angle.
- Apply the laws to navigation and surveying problems.
- Compute the dot product of two vectors and use it to find the angle between them.
- Decide whether two vectors are orthogonal, and find the value that makes them so.
- Find the projection of one vector onto another, and the work done by a force along a displacement.
- Find the magnitude and direction of a resultant force or velocity, including a plane in a wind and a boat in a current.