Students explore the proofs of the Laws of Sine and Cosine, investigate various cases where they are utilized, and apply them to solve problems.

• 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

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. This activity relies on the visuals and interactive nature of the LawsSineCosine.tns file.