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Applications of the Sine Rule and Cosine Rule
See how the sine rule and cosine rule solve triangles and real-life problems, from surveying distances to navigation, with clear worked steps.
What You'll Learn
The sine rule links each side of a triangle to the sine of its opposite angle and works best when you know a matching angle-side pair.
The cosine rule connects all three sides with one angle and is the tool of choice when you know two sides and the included angle, or all three sides.
Word problems about distances, bearings, and surveying almost always reduce to a triangle that needs one of these two rules to solve.
A negative cosine value signals an obtuse angle, which is why understanding angle signs matters before choosing an answer.
The sine rule can produce two possible triangles from the same data, so every answer must be checked for this ambiguous case.
What You'll Practice
1
Solving bearing problems with given distances and directional angles
2
Finding unknown distances in triangles using sine and cosine laws
3
Working through ambiguous SSA cases with two triangle solutions
4
Multi-step problems combining bearings, distances, and angle calculations
Why This Matters
The sine and cosine laws are essential for real-world navigation, surveying, and distance estimation. Whether you're working in aviation, marine navigation, engineering, or GPS technology, these tools let you solve practical problems involving indirect measurements and directional bearings.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Law of Sines
Law of Cosines
Bearings
Ambiguous Case
Triangles
Distance Problems
Navigation
Trigonometry
NL Curriculum Aligned