Download Solving Oblique Triangles Oblique

Today
Wed. Mar 29
MATH 128
Ryan Hansen
Section 9.1 & 9.2
Solve
tan
feet
1
Right Triangle Applications
•
Solving Oblique Triangles
•
Which Are Unique?
•
Law of Sines
Solve
If a building 300 feet tall casts a shadow 50 feet long.
What is the angle of elevation of the Sun?
300
•
300
50
⇥
A security camera is mounted on a wall 9 feet above the
floor. What is its angle of depression if the camera
is directed at a spot 6 feet above
the floor and 12 feet from the wall?
12 feet
tan
1
6 feet
50 feet
4
= sin
6+x
2
=
x
Find .
38.9424
3 feet
80.5377
Solve
3
12
⇥
12 feet
14.0362
x
4
2
=
6+x
x
4x = 12 + 2x
2x = 12
x=6
sin
4
2
=
= sin
6
4
12
1
4
12
⇥
19.4712⇥
Oblique
Solving Oblique Triangles
Not Right
Find All Information
a
Solving Oblique
Triangles
c
Acute
a
Obtuse
b
c
b
Which Are Unique?
(cont.)
Which Are Unique?
Angles
Sides
c
a
b
c
a
2 Angles Given?
Always Unique!
A
Which Are Unique?
(cont.)
1 Angle Given?
S
S
A
A
ASA
S
S
b
SAS
S
ASS
A
Need 3
A
A
SAA
Which Are Unique?
(cont.)
S
Law Of Sines
Law Of Sines - Why?
No Angles Given
c
a
c
S
S
h
a
b
S
sin
a
SSS
Solve
sin
h
h 1
= · =
a
ac
c a
sin ⇥
sin ⇤
=
=
b
c
You Try
=
sin ⇥
h 1
h
= · =
c
a c
ac
Solve
↵ = 44.42 , a = 5, b = 4, c = 7
= 30 , ⇥ = 70 , a = 5
7
30
c
b
= 180
= 80
30
70
6
70
5
sin 30
sin 70
=
5
b
5 sin 70
b=
9.40
sin 30
sin 30
sin 80
=
5
c
5 sin 80
c=
9.85
sin 30
30
100
sin(44.42 )
sin
=
5
7
7 sin(44.42 )
= sin
5
= 78.48652061
or 101.51347939
5
44.42
4
sin(44.42 )
sin
=
5
4
= 34.05096775
or 145.94903225
`
Solving
Law
Oblique
Unique
Of Sines
Triangles
Multiple
Solutions
- ASS
S
A
A
c
Find All Information S
Sa
c
ASAS
a
c
S
A
S sin
b SAS
a
b
=
S
A
Caution:
Rounding
aA
Errors!!!
SAA
A
bS
sin ⇥
sin ⇤S
=Don’tSSSforget
b your homework!!!
c