Download Unit 8 Law of Sines and Cosines

Unit 8 Law of Sines and Cosines
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Trigonometry and Analytical Geometry
September
6 weeks
Published
Enduring Understandings
When you are given two sides and the included angle for a triangle you can use the law of cosines to solve the triangle.
When you are given two sides and the opposite angles for an oblique triangle you can use the law of sines to solve the
triangle.
The law of cosines and the law of sines can be used in conjunction with each other to solve an oblique triangle.
Use properties of the law of the sines and cosines to find the area of an oblique triangle.
Essential Questions
What is the relationship between an angle and the sides of an oblique triangle?
How do we use the law of sines and the law of cosines to solve for unknown measurements in an oblique triangle?
How do we find the area of an oblique triangle?
Content
Vocabulary:
Oblique triangles
Law of sines
Law of cosines
AAS
ASA
SSA
SSS
SAS
Ambiguous case
Heron's Formula
Skills
Use the law of sines to find the sides and angles of a triangle (AAS, ASA, SSA, SSS, SAS)
Use the law of cosines to find the sides and angles of a triangle (SSS, SAS)
Solve triangle area problems using trigonometry and Heron's Formula.
Apply law of sines, law of cosines, and area of a triangle to application problems
Resources
Standards
CCSS.Math.Content.HSG-SRT
Similarity, Right Triangles, and Trigonometry
CCSS.Math.Content.HSG-SRT.D
Apply trigonometry to general triangles
CCSS.Math.Content.HSG-SRT.D.9
Derive the formula � = 1/2 �� sin(�) for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to the opposite side.
CCSS.Math.Content.HSG-SRT.D.10
Prove the Laws of Sines and Cosines and use them to solve problems.
CCSS.Math.Content.HSG-SRT.D.11
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).