Solve Triangles (SAS): Solve for an Unknown Side
Objective: Apply the Law of Cosines: SAS
Solve Triangles (SAS): Solve for an Unknown Side
When you know two sides and an included angle of a triangle (SAS), you can use the Law of Cosines to solve for the other side. Consider the triangle ABC with the measures in the table.
C
b
a
A=35? B=
C=
a=
b=50
c=69
A
B
c
Since we know angle A we use a2 = b2 + c2 - 2bc cos A from the Law of Cosines
a2 = b2 + c2 - 2bc cos A a = b2 + c2 - 2bc cos A a = 502 + 692 - 2(50)(69) cos 35 a 40.1104836
Now use the Law of Sines to solve for B.
sin B = sin A
b
a
sin B = sin 35 50 40.1104836
B = sin-150 sin 35 45.64o 40.1104836
Note that we store that value in "x" for our next computation.
And C 99.36o
A=35? B45.64? C99.36?
a40.11 b=50
c=69
Objective: Apply the Law of Cosines: SAS
Solve Triangles (SSS): Solve for an Unknown Angle
When you know three sides of a triangle (SSS), you can use the Law of Cosines to solve for an angle. Consider the triangles ABC with the measures in the table.
C
b
a
A
B
c
A=
a=40
B=
b=50
C=
c=70
We can solve for angle A using a2 = b2 + c2 - 2bc cos A
a2 = b2 + c2 - 2bc cos A
cos A = b2 + c2 - a2 2bc
A
=
cos-1
b2
+ c2 - 2bc
a2
A
=
cos-1
502 + 702 - 402 2(50)(70)
A 34.05
Now we could use the Law of Sines or Cosines to solve for B. We will use b2 = a2 + c2 - 2ac cos B
cos B = a2 + c2 - b2 2ac
B
=
cos-1
a2
+ c2 - 2ac
b2
B
=
cos-1
402 + 702 - 502 2(40)(70)
B 44.42
Note that we store that value in "A" for a later computation.
And C 101.54o
A34.05?
a=40
B44.42?
b=50
C101.54 ?
c=70
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