Algebra II
Honors
(Pre-Calculus)
6.1, 6.2: Law of
Sines & Cosines
Quiz 6.1-6.2: Tues,
5/29
Solving triangles (other than right triangles)
 Law
of Sines
a
b
c


sin A sin B sin C
 Law
2
The formula you choose
depends on the
information you are
given.
B
of Cosines
a  b  c  2bc cos A
2
2
b  a  c  2ac cos B
2
2
c
a
2
c 2  a 2  b 2  2ab cos C
A
b
C
Solve the triangle with the following:
B
c
A
A  36 , B  48 , a  8
a
b
C
Solve the triangle with the following:
B
c
A
a  4, b  7, A  42
a
b
C
Solve the triangle with the following:
B
c
A
a  9, b  7, c  5
a
b
C
Solve the triangle with the following:
B
c
A
b  15, c  10, A  115
a
b
C
Solve the triangle with the following:
B
c
A
a  7, b  6, B  30
a
b
C
Do Now: Solve the triangle with the following.
B
c
A
a  22, b  12, A  42
a
b
C

Area of a Triangle
B
c
A
1
1
1
Area  bc sin A  ab sin C  ac sin B
2
2
2
a
b
Heron’s Formula
C
Area 
ss  a s  b s  c 
where s  a  b  c  2
Find the area of the triangle:
B
c
A
a  6, b  10, C  110
a
b
C
Find the area of the triangle:
B
c
A
a  2, b  3, c  4
a
b
C
Find the area of the triangle:
B
c
A
b  67, c  85, A  38 45
a
b
C
Find the area of the triangle:
B
c
A
a  5, b  9, c  10
a
b
C
Example
Forest Ranger Rich is at an observation point A along
a straight road. He observes a fire in the direction 32o
east of north. Forest Ranger Sara is at a second
observation point B 10 miles due east of Rich. Sara
sights the same fire 48o west of north. Find the
distance from each ranger to the fire and find the
shortest distance from the fire to the road.
Example
In major league baseball, the four bases form a
square whose sides are 90 feet. The front edge of the
pitching rubber on which the pitcher stands, is 60.5
feet from home plate.
a.) Find the distance from the front edge of the
pitching rubber to 1st base.
b.) Find the measure of the angle formed by 1st
base, the pitching rubber and home plate.
Example
The course for a boat race starts at a point and
proceeds in the direction S52oW to a point B, and in
the direction S40oE to point C, and finally back to
point A. The point C lies 8 km directly south of point
A. What is the length of the total course?