April 29, 2014
7-1
Oblique Triangles and
the Law of Sines
7-2
The Law of Cosines
We must have certain information before we can begin to solve an
oblique triangle. There are three cases in which we use the Law of
Sines.
Case 1: AAS
Case 2: ASA
Case 3: SSA
We have already learned how to solve triangles. What kind of
triangles have we solved? What does it mean to solve a triangle?
Today we are going to learn how to solve oblique triangles.
What makes a triangle an oblique triangle?
We have two formulas that we use to help us solve oblique triangles:
Law of Sines
Law of Cosines
You will need to know these formulas from memory!
Law of Sines
γ
a
b
Let's use this triangle to
remember what each of these
cases looks like.
α
β
c
Example 1
What case is this?
Solve the triangle with a = 7.0m, α = 110º and γ = 33º
Example 2
What case is this?
Solve the triangle with c = 17 mi., α = 80º and β = 32º
Example 1 - on your own
Example 2 - on your own
Solve the triangle with b = 30 ft., α = 105º and β = 43º
Solve the triangle with a = 12 in., β = 85º and γ = 60º
April 29, 2014
Example 3
What case is this?
Solve the triangle with a = 23 ft., b, = 11 ft., and α = 122º
Case 3: SSA
This case is also called the ambiguous case. If the angle that we are
given is an acute angle, then we might have one triangle, two
triangles, or no triangles at all, with the given information. If the
given angle is obtuse, then we might have one triangle or no triangles
at all.
Let's look at some examples of all of this!
Example 4
What case is this?
Solve the triangle with a = 8.1 m., b, = 8.3 m., and α = 72º
Example 5
What case is this?
Solve the triangle with a = 6, b, = 8, and α = 107º
Example 5 - on your own
Solve the triangle with a = 48 mm., c = 17 mm., and α = 133º
We must have certain information before we can begin to solve an
oblique triangle. There are two cases in which we use the Law of
Cosines.
Case 1: SAS
Case 2: SSS
γ
a
b
Let's use this triangle to
remember what each of these
cases looks like.
α
β
c
Law of Cosines
April 29, 2014
Example 6
What case is this?
Solve the triangle with a = 13, c = 6 and β = 20º
Example 7
What case is this?
Solve the triangle with a = 8, b = 6 and c = 7
Example 6 - on your own
What case is this?
Solve the triangle with b = 4.2, c = 1.8 and α = 35º
Example 7 - on your own
What case is this?
Solve the triangle with a = 5, b = 7 and c = 8
Homework
pp. 369-370
#s 7, 15, 19, 21-29 odd, 46
pp. 379-380
#s 1-8 all, 9, 11, 13, 21, 27, 33, 48