1. Section 6.1
Law of Sines

2. Objective By following instructions students will be able to:
Use the Law of Sines to solve oblique triangles (AAS, ASA, or SSA).
Find areas of oblique triangles.
Use the Law of Sines to model and solve real-life problems.

3. Oblique Triangles C Triangles that have no right angles.
When Solving, you will need:
AAS or ASA
SSA
SSS
SAS a b A B c

4. Law of Sines
If triangle ABC is a triangle with sides a, b, and c, then: or

5. Example 1: Given Two Angles and One Side-AAS
In triangle ABC, , , and . Find the remaining angle and side.

6. Example 2: Given Two Angles and One Side-AAS
A pole tilts toward the sun at an angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is How tall is the pole?

7. The Ambiguous Case – SSA
If Angle A is ACUTE
Consider a triangle in which you are given a, b, and A; (h = b sinA)
One Triangle A b
h a A b a h

8. The Ambiguous Case – SSA
If Angle A is ACUTE
Consider a triangle in which you are given a, b, and A; (h = b sinA)
Two Triangles
No Triangle A b a a h A b a h

9. The Ambiguous Case – SSA
If Angle A is OBTUSE
Consider a triangle in which you are given a, b, and A; (h = b sinA)
No Triangle
One Triangle A b a A b a

10. Example 3: Single Solution Case- SSA
For the triangle, , , and . Find the remaining side, and angles. A
b=12in
a=22in C B c

11. Example 4: No Solution Case- SSA
Show that there is no triangle for which, , , and A
b=25
a=15 h

12. Example 5: Two Solution Case- SSA
Find two triangles for which , , and

13. Area of an Oblique Triangle
Consider a triangle in which you are given a, b, and A; (h = b sinA)
The area of any triangle is Hence, C C A b a A b a h h B c c B

14. Example 6: Finding the Area of an Oblique Triangle
Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of C
b=52m
a=90m

15. Example 7: An Application of the Law of Sines
The course for a boat race starts at point A and proceeds in the direction South West to point B, then in the direction South East to point C, and finally back to A. The point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.

16. Revisit Objective Did we…
Use the Law of Sines to solve oblique triangles (AAS, ASA, or SSA)?
Find areas of oblique triangles?
Use the Law of Sines to model and solve real-life problems?

17. Homework
Pg 434 #1, 4, 5, 7, 8, 12-14, 19, 20