6.1 laws of sines. the laws of sine can be used with oblique triangle oblique triangle is a triangle...
Post on 13-Dec-2015
219 Views
Preview:
TRANSCRIPT
6.1 Laws of Sines
The Laws of Sine can be used with Oblique triangle
Oblique triangle is a triangle that contains no right angle.
A
B
C
a
b
c
The Laws of Sines
A
B
C
a
b
c
C
c
B
b
A
a
sinsinsin
Using the Law of Sines
Given: How do you find angle B?
aA
B
C
c
b
a
Bm
Cm
Am
6.21
7.16
4.102
b
c
Using the Law of Sines
Given: How do you find side b?
aA
B
C
c
b
a
Bm
Cm
Am
6.21
9.60
7.16
4.102
b
c
Using the Law of Sines
Given: How do you find side b?
aA
B
C
c
b
a
Bm
Cm
Am
6.21
9.60
7.16
4.102
9.60sin4.102sin
6.21 b
b
c
Using the Law of Sines
Given: How do you find side b?
aA
B
C
3.19
7.102sin
9.60sin6.21
9.60sin4.102sin
6.21
b
b
b
c
b
a
Bm
Cm
Am
3.19
6.21
9.60
7.16
4.102
b
c
Using the Law of Sines
Given: How do you find side c?
aA
B
C
c
b
a
Bm
Cm
Am
3.19
6.21
9.60
7.16
4.102
7.16sin4.102sin
6.21 c
b
c
Using the Law of Sines
Given: How do you find side c?
aA
B
C
c
b
a
Bm
Cm
Am
3.19
6.21
9.60
7.16
4.102
36.6
4.102sin
7.16sin6.21
7.16sin4.102sin
6.21
c
c
c
b
c
The Ambiguous Case
Look at this triangle.
If we look at where angle A
Is Acute
A B
C
b a
h
Abh sin
The Ambiguous Case
Look at this triangle.
If we look at
If a = h, then there is one triangle
A B
C
bahAbh sin
The Ambiguous Case
Look at this triangle.
If we look at
If a < h, then there is no triangle
A B
C
ba
hAbh sin
The Ambiguous Case
Look at this triangle.
If we look at
If a > b, then there is one triangle
A B
C
b a
hAbh sin
The Ambiguous Case
Look at this triangle.
If we look at
If h< a <b, then there is two triangles
A B
C
b a
hAbh sin'B
The Ambiguous Case
Do you remember the Hinge Theorem from Geometry.
Given two sides and one angle, two different triangles can be made.
http://mrself.weebly.com/5-5-the-hinge-theorem.html
15 151111
42 42
The Ambiguous Case
Where Angle A is Obtuse.
If a ≤ b, there is no
triangle
A
a
b
The Ambiguous Case
Where Angle A is Obtuse.
If a > b, there is one
triangle
A
a
b
Area of an Oblique triangle
Using two sides and an Angle.
SinBacArea
SinCabArea
SinAbcArea
2
1
2
1
2
1
Find the missing Angles and Sides
Given: 5,8,36 baA
Find the missing Angles and Sides
Given:
5.122
1805.2136
C
C
5,85.122,5.21,36 baCBA
Find the missing Angles and Sides
Given: 5,85.122,5.21,36 baCBA
48.11
36
5.1228
36
8
5.122
c
Sin
Sinc
SinSin
c
HomeworkHomework
Page 416 Page 416
##1, 7, 13, 19,1, 7, 13, 19,
25, 31, 37,25, 31, 37,
43, 4943, 49
Homework
Page 416
# 4, 10, 16, 22,
28, 34, 40,
46, 52
top related