This document discusses the Law of Sines and how to apply it to solve oblique triangles. It defines an oblique triangle as one with no right angles. The Law of Sines can be used to solve triangles in Cases 1 and 2, where two angles and one side or two sides and one angle are given. It presents the Law of Sines theorem that the ratio of the sine of any angle of a triangle to the side opposite it is equal to the ratios of the sines of the other angles to their opposite sides.

1. The Law of Sines
Module: Learning Area Methodology 2A
Initials and Surname: CG Nkosi
Student number: 201142269

2. Lesson outcomes
 At the end of the lesson learners should be able to:
 identify the characteristics of oblique triangles.
 Apply the Law of Sines.
 Know all the Cases of the Law of Sines.

3. If none of the angles of a triangle is a right
angle, the triangle is called oblique.

4. To solve an oblique triangle means to find the
lengths of its sides and the measurements of
its angles.
Case 1: you are given two angles and one
side

5. Case 2: you are given two sides and one angle
which is corresponded with one side.

6. Case 3: you are given two sides and one angle
which is corresponded with the unknown
side.

7. Case4: you are given the sides only

8. The Law of Sines is used to solve triangles in which
Case 1 or 2 holds. That is, the Laws of Sines is used
to solve SAA, ASA, or SSA triangles.
 Theorem Law of Sines
For a triangle with sides a, b, c, and opposite angles
, , , respectively

10. To find side b, we apply the Law of Sines
formula.

11. Find the next unknown side (c)and the
angle( ), is your activity.
 Hint: use the Law of Sines