Download Law of Sines - Petal School District

Advanced Geometry
Trigonometry
Lesson 4
The Law of Sines
C
a
b
A
c
B
C
b
A
C
x
a
y
B
c
x
sin A 
b
a
b
A
x
sin B 
a
B
c
y
sin B 
c
y
sin C 
b
b sin A  x a sin B  x
c sin B  y b sin C  y
b sin A  a sin B
c sin B  b sin C
sin A sin B

a
b
sin B sin C

b
c
The Law of Sines
sin A sin B sin C


a
b
c
Example: Find p. Round to the nearest tenth.
Example: Find m∠L to the nearest degree in
∆LMN if n = 7, l = 9, and m∠N = 43.
Example: Solve ∆DEF if m∠D = 112, m∠F = 8,
and f = 2. Round angle measures to the nearest
degree and side measures to the nearest tenth.
Example: Solve ∆HJK if m∠J = 32, h = 30,
and j = 16. Round angle measures to the nearest
degree and side measures to the nearest tenth.
Example: Three cities form the vertices of a triangle.
The angles of the triangle are 40°, 60°, and 80°.
The two most distant cities are 40 miles apart.
How close are the two closest cities to the nearest
tenth of a mile?