The Law of Sines

1
6.1

• The Law of Sines

2
Quick Review

3
Quick Review Solutions

4
What youll learn about

• Deriving the Law of Sines
• Solving Triangles (AAS, ASA)
• The Ambiguous Case (SSA)
• Applications
• and why
• The Law of Sines is a powerful extension of the
  triangle congruence theorems of Euclidean
  geometry.

5
Law of Sines

6
(No Transcript)
7
Example Solving a Triangle Given Two Angles and a
Side

8
Example Solving a Triangle Given Two Angles and a
Side

9
(No Transcript)
10
(No Transcript)
11
Example Solving a Triangle Given Two Sides and an
Angle (The Ambiguous Case)

12
Example Solving a Triangle Given Two Sides and an
Angle (The Ambiguous Case)

13
Example Finding the Height of a Pole

14
Example Finding the Height of a Pole

15
6.2

• The Law of Cosines

16
Quick Review

17
Quick Review Solutions

18
What youll learn about

• Deriving the Law of Cosines
• Solving Triangles (SAS, SSS)
• Triangle Area and Herons Formula
• Applications
• and why
• The Law of Cosines is an important extension of
  the Pythagorean theorem, with many applications.

19
Law of Cosines

20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
Example Solving a Triangle (SAS)

24
Example Solving a Triangle (SAS)

25
Area of a Triangle

26
Herons Formula

27
Example Using Herons Formula

• Find the area of a triangle with sides 10, 12, 14.

28
Example Using Herons Formula

• Find the area of a triangle with sides 10, 12, 14.

29
Chapter Test

30
Chapter Test

31
Chapter Test
9. A hot-air balloon is seen over Tucson,
Arizona, simultaneously by two observers at
points A and B that are 1.75 mi apart on level
ground and in line with the balloon. The angles
of elevation are as shown here. How high above
ground is the balloon?

10. A wheel of cheese in the shape of a right
circular cylinder is 18 cm in diameter and 5 cm
thick. If a wedge of cheese with a central angle
of 15º is cut from the wheel, find the volume of
the cheese wedge.
32
Chapter Test Solutions

33
Chapter Test Solutions

34
Chapter Test Solutions
9. A hot-air balloon is seen over Tucson,
Arizona, simultaneously by two observers at
points A and B that are 1.75 mi apart on level
ground and in line with the balloon. The angles
of elevation are as shown here. How high above
ground is the balloon?

0.6 mi
10. A wheel of cheese in the shape of a right
circular cylinder is 18 cm in diameter and 5 cm
thick. If a wedge of cheese with a central angle
of 15º is cut from the wheel, find the volume of
the cheese wedge.
405p/2453.01