The Law of Cosines
B
a  b  c  2bc cos A
2
2
2
c
b  a  c  2ac cos B
2
2
2
c  a  b  2ab cos C
2
2
2
A
When to use the Law of Cosines:
 SSS
 SAS
a
b
C
Students will be able to…use the Law of
Sines to solve triangles and real-world
problems.
9.3: Law of Sines
A = ½ a•b•sin(C) = ½ a•c•sin(B) = ½ b•c•sin(A)
-divide each side by “½abc”
A
sin A = sin B = sin C
a
b
c
C

Works in the following cases:
› ASA
› AAS
› SSA
c
b
a
B
Find p. Round to the nearest tenth.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer:
to the nearest degree in
,
Law of Sines
Cross products
Divide each side by 7.
Solve for L.
Use a calculator.
Answer:
.
Angle Sum Theorem
Add.
Subtract 120 from each side.
Since we know
and f, use proportions involving
To find d:
Law of Sines
Substitute.
Cross products
Divide each side by sin 8°.
Use a calculator.
To find e:
Law of Sines
Substitute.
Cross products
Divide each side by sin 8°.
Use a calculator.
Answer:
A 46-foot telephone pole tilted at an angle of from
the vertical casts a shadow on the ground. Find the
length of the shadow to the nearest foot when the
angle of elevation to the sun is
Draw a diagram Draw
Then find the
Since you know the measures of two angles of the
triangle,
and the length of a side
opposite one of the angles
you
can use the Law of Sines to find the length of the shadow.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer: The length of the shadow is about
75.9 feet.
A 5-foot fishing pole is anchored to the edge of a
dock. If the distance from the foot of the pole to the
point where the fishing line meets the water is 45 feet,
about how much fishing line that is cast out is above
the surface of the water?
Answer: About 42 feet of the fishing line that is cast out
is above the surface of the water.