1. Laws of Sines

2. The Laws of Sine can be used with Oblique triangle
Oblique triangle is a triangle that contains no right angle.

3. The Laws of Sines Or

4. Example 1
You are given a triangle, ABC, with angle A = 70°, angle B = 80° and side a = 12 cm. Find the measures of angle C and sides b and c. A C B
70°
80°
a = 12 c b

5. Using the Law of Sines
Given:

10. The Ambiguous Case Look at this triangle. If we look at where angle A
Is Acute

11. The Ambiguous Case Look at this triangle. If we look at
If a = h, then there is one triangle

12. The Ambiguous Case Look at this triangle. If we look at
If a < h, then there is no triangle

13. The Ambiguous Case Look at this triangle. If we look at
If a > b, then there is one triangle

14. The Ambiguous Case Look at this triangle. If we look at
If h< a <b, then there is two triangles

15. The Ambiguous Case Do you remember the Hinge Theorem from Geometry.
Given two sides and one angle, two different triangles can be made.

16. The Ambiguous Case Where Angle A is Obtuse. If a ≤ b, there is no
triangle

17. The Ambiguous Case Where Angle A is Obtuse. If a > b, there is one
triangle

18. Area of an Oblique triangle
Using two sides and an Angle.

19. Find the missing Angles and Sides
Given:

20. Find the missing Angles and Sides
Given:

21. Find the missing Angles and Sides
Given: