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The Law of Cosines
•
Section 2.2
49
Exercises
For Exercises 16, solve the triangle
△
ABC
.
1.
A
=
60
◦
,
b
=
8,
c
=
12
2.
A
=
30
◦
,
b
=
4,
c
=
6
3.
a
=
7,
B
=
60
◦
,
c
=
9
4.
a
=
7,
b
=
3,
c
=
9
5.
a
=
6,
b
=
4,
c
=
1
6.
a
=
11,
b
=
13,
c
=
16
7.
The diagonals of a parallelogram intersect at a 42
◦
angle and have lengths of 12 and 7 cm. Find
the lengths of the sides of the parallelogram. (
Hint: The diagonals bisect each other.
)
8.
Two trains leave the same train station at the same time, moving along straight tracks that form
a 35
◦
angle. If one train travels at an average speed of 100 mi/hr and the other at an average
speed of 90 mi/hr, how far apart are the trains after half an hour?
9.
Three circles with radii of 4, 5, and 6 cm, respectively, are tangent to each other externally. Find
the angles of the triangle whose vertices are the centers of the circles.
10.
Find the length
x
of the diagonal of the quadrilateral in Figure 2.2.3 below.
2
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 Fall '11
 Dr.Cheun
 Calculus, Law Of Cosines

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