The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It then gives examples of using the Law of Sines to find specific values like side lengths and triangle areas.

1. Law of Sines May 10, 2011
The Law of Sines
Objectives:
1. To apply the Law of Sines
2. To develop problem‐solving skills.
The Law of Sines can be used to find missing parts of any triangles!
Law of Sines
In ΔABC: a, b, & c represent
the measures of the sides
opposite the angles with C
measures A, B, & C. b a
THEN:
sin A = sin B = sin C A c B
a b c
The Law of Sines can be used to solve a triangle in the following cases:
Case 1: You know the measure of two angles and any side
of a triangle.
What is looks like:
Case 2: You know the measures of 2 sides and an angle
opposite one of these sides of the triangle.
What is looks like:
HW Law of Sines Wkst 1

2. Law of Sines May 10, 2011
Find b. Round to the nearest tenth.
C
68o 3
37o
A b B
Triangle Area
You can find the area of a triangle by using the follwing:
A = 1/2 ab sinC
where a & b are the lengths of 2 sides and C is the angle
between these two sides.
b
h
C a
Find the area
9
50o
18
HW Law of Sines Wkst 2

3. Law of Sines May 10, 2011
Find p. Round to the nearest tenth.
Then, find the area of ΔPQR
Q
8
17o 29o
P R
What is the area of ΔLMN if n = 7, l = 9, and
measure of angle N = 43o?
HW Law of Sines Wkst 3

4. Law of Sines May 10, 2011
A house is built on a triangular plot of land. Two sides of the
plot are 160 feet long, and they meet at an angle of 85o. If a
fence is to be placed along the perimeter of the property, how
much fencing materials is needed?
How many square feet of property does the landowner possess?
HW Law of Sines Wkst 4

5. Law of Sines May 10, 2011
HW: Law of Sines Worksheet
HW Law of Sines Wkst 5