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Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Geometry and Trigonometry

Law of Sines and Cosines


  • Students will derive, discuss and apply the Law of Sines and the Law of Cosines.
  • Students will practice applying these laws, and the area of a triangle using trigonometry, to real world situations.
  • Students will try to make a connection with how to understand these topics in IB Mathematics courses and on their final assessments.


  • Proofs
  • Oblique Triangles
  • Law of Sines
  • Law of Cosines
  • Right Triangle Trigonometry

About the lesson

Throughout history, mathematicians from Euclid to al-Kashi to Viète have derived various formulas to calculate the sides and angles of non-right (oblique) triangles. al-Kashi used these methods to find the angles between the stars back in the 15th century. Both the famous Laws of Sines and Cosines are used extensively in surveying, navigation, and other situations that require triangulation of non-right triangles. In this activity, you will explore the proofs of the Laws, investigate various cases where they are used, and apply them to solve problems. If time permits, the teacher can demonstrate how to create and manipulate sides and angles of triangles using Cabri Jr. on the handheld. This may help students in understanding the discussion questions about moving angle C.

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