Notes on 8-6

1. SECTION 8-6
Law of Sines
Jim Smith JCHS
3108.4.49
Use the Law of Sines to find missing side lengths and/or
angle measures in non-right triangles

2. A Car Runs Into A Telephone Pole And
Knocks It Off Perpendicular To The
Ground By 9°. If The Pole’s Shadow
Is 57 Feet Long And The Angle Of
Elevation From The Ground To The
Top
Of The Pole Is 48°, How Can We Find
The Height Of The Pole?

3. What method did we use to find
the height of a tree?
What measures did we need to
find the height of a tree or a pole?
If the pole is leaning at an angle,
why can’t we use sin, cos, or tangent?

4. The Law Of Sines Allows Us To Work
With Triangles Other Than Right
Triangles.

5. In A Triangle, The Ratio
Of The Sine Of An Angle And
The Length Of The Side Opposite
That Angle Are The Same For
Each Pair Of Angles And Sides.
They are ___________________
Proportional

6. A
B
C
c a
b
c
C
b
B
a
A sin
sin
sin


Students will be able to write
the law of Sines formula

7. Students will be able
to find the missing side of
a non-right triangle
A
B C
85°
70°
X
15
X
70
sin
15
85
sin

)
70
(sin
15
)
(
85
sin 
X
85
sin
)
70
(sin
15
85
sin
)
(
85
sin

X
85
sin
)
70
(sin
15

X
15
.
14

X
AAS
ACT FORM

8. X
70
sin
15
85
sin

)
70
(sin
15
)
(
85
sin 
X
85
sin
)
70
(sin
15
85
sin
)
(
85
sin

X
85
sin
)
70
(sin
15

X
15
.
14

X
X
9396
.
15
9961
.

)
9396
(.
15
9961
. 
X
9961
.
10
.
14
9961
.
9961
.

X
15
.
14

X
“Another way to skin a cat”

9. Back To The Car And
Telephone Pole
A Car Runs Into A Telephone Pole And
Knocks It Off Perpendicular To The
Ground By 9°. If The Pole’s Shadow
Is 57 Feet Long And The Angle Of
Elevation From The Ground To The
Top
Of The Pole Is 48°, How Can We Find
The Height Of The Pole?

10. 9°
57
48°
Do you know how to solve it now?

11. 9°
48°
57
A
B
C
x
9
90

BCA
81°
81
48
180 


ABC
51°
57
51
sin
48
sin

x
48
sin
57
)
(
51
sin 
x
51
sin
48
sin
57

x
51
.
54

x

12. Let’s find an angle…
Look at a right triangle from
last week first …
10
22
22
10
x
of
sin 
22
10
sin
2nd 

 00
.
27
x
x

13. 5 3
x 50°
5
50
sin
3
sin

x
)
50
(sin
3
)
(sin
5 
x
5
)
50
(sin
3
sin 
x
5
)
50
(sin
3
sin
2nd 

 36
.
27
x
Students will be able
to find the missing angle of
a non-right triangle
Add This

14. x
17
92°
14
17
92
sin
14
sin

x
17
9993
.
14
sin

x
99
.
13
)
(sin
17 
x
17
99
.
13
sin 
x
)
7
1
(13.99
sin
2 
nd

 38
.
55
x

15. SSA be careful