Download Lesson 6.1 Law of Sines

Lesson 6.1
Law of Sines
Draw any altitude from a vertex and label it k. Set up equivalent trig
equations not involving k, using the fact that k is equal to itself
Use the Law of Sines in oblique triangles (no right angle)
The phrase “solve a triangle” means to find all unknown sides or angle.
Example 1 Solve the triangle
Special Cases:
Cannot use Law of Sines when given SSS, AAA, or SAS
So that leaves 3: ASA, AAS, ASS
ASA & AAS give unique solutions
ASS (or SSA if you prefer) can give 3 possibilities:
1) Single Solution
2) Two Solutions
3) No Solution
Example 2 Solve the triangle
A = 60o, a = 9, c = 10
Example 3 Solve the triangle
A = 42o, a = 22, c = 12
Example 4 Solve the triangle
A = 110o, a = 125, c = 200
2 solutions: 2 angles solved from equation give 3 angles that add to 1800
1 solution: only 1 of 2 angles solved from equation work
No solution: any solved angle does not work or sin (angle) is undefined
Area of Oblique Triangles
Use the formula:
1
Area  base  height
2
In the acute triangle below, c is the base and h is the height
h
h
Problem: h is not given.
Solution: Use trigonometry to find write an equation for h.
Formulas:
1
Area  bc sin A
2
1
Area  ac sin B
2
1
Area  ab sin C
2
Remember…
Use all 3 letters
2 little letters (sides), 1 big (angle)
Example Find the area of the triangle.
Problem Set 6.1