Part II: Which Method?
Directions:
Which method, Right Triangle Trigonometry, the Law of Cosines, or the
Law of Sines, would be
best
to use as the first step in solving triangle
ABC
under the
given conditions and why?
Example 3:
B
=
65
◦
, a
=
6, b
=
7
.
Method:
Law of Sines
Why:
We are given “SSA.”
Example 4:
a
=
3, C
=
90
◦
, c
=
5
.
Method:
Right Triangle Trigonometry (i.e. the Pythagorean Theorem and the definitions
of sine, cosine, and tangent)
Why:
Triangle
ABC
is a right triangle
Now you try:
5. Assume the angles of a triangle are labeled with the capital letters
A, B,
and
C,
and the side
opposite an angle is labeled with the corresponding lowercase letter
a, b,
or
c.
Which method
, “Right Triangle Trigonometry”, the “Law of Cosines”, or the “Law of Sines”,
would be
best
to use as the first step in solving triangle
ABC
under the given conditions?
To explain
why
, choose one of “right triangle”, “SSS”, “SAS”, “SSA”, or “AAS”.
Do not solve
the triangles.
(a)
b
=
30
,
c
=
47
,
C
=
52
◦
(d)
a
=
28
,
b
=
43
,
c
=
53
Which Method? Why?
Which Method? Why?
(b)
B
=
37
◦
,
c
=
41
,
C
=
33
◦
(e)
a
=
42
,
b
=
45
,
C
=
161
◦
Which Method? Why?
Which Method? Why?
(c)
A
=
54
◦
,
c
=
29
,
C
=
90
◦
(f)
a
=
45
,
A
=
90
◦
,
b
=
32
Which Method? Why?
Which Method? Why?
7