April 4th
copyright2009merrydavidson
Happy Summer Birthdays to:
Timmy Manley: 7/5th
Andrew Krasner: 8/14th
CALCULATOR TODAY
OBLIQUE TRIANGLES
6.1 & 6.2
A triangle with NO right angles.
A
little a is
c
across from
b
Big A
C
a
B
ANGLES/CAPITAL LETTERS
sides/small letters
put calculator in
degree mode
SOLVE the triangle
Means to find the length
of all sides and the
measure of all angles.
To solve oblique triangles two
pieces of information are
needed and a TRIG FUNCTION.
Round sides to the nearest
TENTH and angles to the nearest
DEGREEunless otherwise noted.
This formula states that the ratio of any side
of a triangle to the sine of the angle opposite
that side is a constant (proportional) for a
given triangle.
LAW OF SINES
(you will use 2 of
the 3 sections to
make a
proportion.
Memorize this……..
a
b
c


sin A sin B sin C
EX 1: Given triangle ABC with the
measures shown below, find b?
START with a chart.
C
a=
b=
c=
c=8
A= 49 B=57
B=
C= 74
C=
Fill in what you know
B
49O
57O
8
A
b
8

sin 57 sin 74
Find angle C.
Solve the proportion
bsin74 = 8sin57
b
=
8sin57
approx 7.0
sin74
EX 2: In triangle ABC if
A = 32, B = 57, and c =
14. Find angle C and
sides a and b.
a=
b=
c=
A=
B=
C=
You do this one. In a
minute I will show you
the answer.
a  7.4
b  11.7
C  91
EX 3: In triangle ABC,
A = 1100, b = 7 and a =
9. Find angle B.
a=
b=
c=
A=
B=
C=
B  47
9
7

sin110 sin B
7sin110 = 9sinB
sinB = 7sin110
9
Use sine inverse
1 7 sin110
B  sin (
)
9
EX 4: Given an oblique
triangle with angle
A = 490, and side
a = 8 and side b = 9,
find angle B.
a=
b=
c=
A=
B=
C=
You do this one. In a
minute I will show you
the answer.
B  58
EX 5: Find b
A
7
You can not make a
proportion
b
51O
B
C
10
aa==10
bb==
cc== 7
AA==
BB== 51 CC==
LAW OF COSINES is
used when you can not
make a proportion.
6.2
Memorize these……..
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 –2ac cos B
c2 = a2 + b2 – 2ab cos C
EX 5: Find b
Using the law of cosines…..
A
7
a = 10 b =
c=7
A=
C=
B = 51
b
51O
B
10
C
b2 = a2 + c2 -2ac cos B
b2 = 102 + 72 -2(10)(7) cos 51
b  60.9
EX 6:
SOLVE the triangle.
C
5
Always find the “biggest”
angle first! So find C.
4
A
7
B
c2 = a2 + b2 -2ab cos C
a=4
b=5
c=7
72 = 42 + 52 -2(4)(4) cos C
A=
B=
C=
49 = 41-2(4)(4) cos C
8 = -2(4)(4) cos C
8
C  cos (
)  104
32
1
“store” this to find the
other parts.
EX 6:
SOLVE the triangle.
Now use Law of Sines
C
5
4
to find A or B. Then
use the sum of angles in
a triangle is 180o to
A
7
a=4
b=5
c=7
A=
B=
C = 104
B
find the other angle.
B  44
A  32
EX 7:
SOLVE the triangle.
A
8
b
What should you find
first???
little b
b  7.2
60O
B
C
6
a=
b=
c=
A=
B=
C=
Store this!
Now find angle
A or C.
A  46
C  74
EX 8: Find cos X;
given x = 5, y = 3 and
z = 6 in triangle XYZ.
x=
y=
z=
X=
Y=
Z=
5
cos X 
9
HW: WS
and work on TAKS packet
for additional help on law
of sines and/or cosines, go
to the internet or come in
to see me.