7.2 Day 1 The Law of Sines April 30, 2009
7.2 The Law of Sines
Day 1
Objective - Use the law of
sines to find measures of
sides and angles in
triangles.
Apr 20 ­ 6:57 AM
1
7.2 Day 1 The Law of Sines April 30, 2009
With a right triangle, you can use the trig identities to find missing sides or angles.
tan =
opp
adj
cos
=
adj
hyp
sin
opp
=
hyp
hyp
opp
adj
Apr 18­6:41 PM
2
7.2 Day 1 The Law of Sines April 30, 2009
But what about a triangle that does not have a right angle?
We need some type of strategy to find missing sides and angles.
Apr 18­6:44 PM
3
7.2 Day 1 The Law of Sines April 30, 2009
This is where the Law of Sines comes in...
a
c
β
γ
α
b
Start with any triangle that does not have a right angle.
Notice: The ANGLES are labeled with GREEK LETTERS. We will always label triangles so a is opposite α, b is opposite β, and c is opposite γ.
Apr 18­6:49 PM
4
7.2 Day 1 The Law of Sines April 30, 2009
Law of Sines
(For a triangle with sides a, b, c and opposite
angles α, β, γ, respectively.)
a
sin α
=
c
b
sin β
=
β
c
sin γ
a
γ
α
b
Apr 20 ­ 7:02 AM
5
7.2 Day 1 The Law of Sines April 30, 2009
Law of Sines
(It may also be used in this form.)
sin α
a
=
c
sin β
b
β
=
sin γ
c
a
γ
α
b
Apr 20 ­ 7:02 AM
6
7.2 Day 1 The Law of Sines April 30, 2009
Example #1: Find the missing angles and side lengths.
Find m B
a
b
=
B
4
c
o
36
A
5.6
C
sin A sin B
4 5.6
=
sin 36 sin B
4 sin B = 5.6 sin 36
sin B = 0.82
­1
B = sin 0.82
STACK BOXES HERE
B = 55.4o
Apr 20 ­ 8:43 AM
7
7.2 Day 1 The Law of Sines April 30, 2009
Example #1: Find the missing angles and side lengths.
Find m C
B
4
c
O
36 + 55.4 + C = 180
o
36
A
A + B + C = 180
5.6
C
C = 88.6
O
STACK BOXES HERE
Apr 20 ­ 8:43 AM
8
7.2 Day 1 The Law of Sines April 30, 2009
Example #1: Find the missing angles and side lengths.
B
Find length of side c
o
36
A
a c
=
sin A sin C
4 c
=
sin 36 sin 88.6
4 sin 88.6
c =
sin 36 c = 6.8
4
c
5.6
C
STACK BOXES HERE
Apr 20 ­ 8:43 AM
9
7.2 Day 1 The Law of Sines April 30, 2009
,
:
n
k
e
r
v
o
e
w
4
e
2
m 0 ­ 5)
o
H 9 (1 2, 4
4
3
,
5
9
e
3
g 8, a
p
3
#10
Apr 20 ­ 10:06 AM
10
7.2 Day 1 The Law of Sines April 30, 2009
10. Solve the triangle.
a
γ
b
45o
40o
4
γ = 95o
a ≈ 2.84
b ≈ 2.58
Apr 26­1:51 AM
11