# File ```AGENDA:
Take DG31 --- 15 minutes
Complete Lesson 2 Law of Cosines
Accel Precalc
Unit 7: Extended Trigonometry
Lesson 2: Law of Cosines
EQ:
How do you use Law of Cosines to solve
non-right triangles?
Two Methods to Solve “Oblique Triangles”:
Use the Following Cases for Law of Cosines:
NOTE: This is the same formula
just written 3 different ways!!
Ex 1. Given side b = 12, side c = 20 and A = 40&ordm;.
Find the length of side a to the nearest
integer.
a 2  b 2  c 2  2bc cos A
a 2  12  20  21220 cos 40
2
2
a 2  176.2988
a  13.277  13
Ex. 2 Find the measure of the largest angle, to
the nearest tenth of a degree, of a triangle
whose sides are 9, 12, and 18.
b 2  a 2  c 2  2ac cos B
Looking for an
18
2
 12  9
2
2
angle means
will use…?
 2129you
cos B
182  122  92  2129 cos B
2
2
2
18  12  9   cos B
117.27  B
 2129
2
2
2
117
.
3


B


1 18  12   9  
B
cos 







2
12
9


Ex. 3 In a parallelogram, the adjacent sides measure 40 cm
and 22 cm. If the larger angle of the parallelogram
measures 116&ordm;, find the length of the longer diagonal, to
the nearest integer.
b 2  a 2  c 2  2ac cos B
b  22  40  22240 cos116
2
2
2
b 2  2855.5332
b  53.437  53
USING THE LAW OF COSINES IN AN
APPLICATION (SAS)
A surveyor wishes to find the distance between
two inaccessible points A and B on opposite
sides of a lake. While standing at point C, she
finds that AC = 259 m, BC = 423 m, and
angle ACB measures 132&deg;40′. Find the
distance AB.
Example 4
 AB 2   AC 2  BC 2  2 AC BC  cos C
 AB 2  2592  4232  2259423 cos13240'
AB  628 m
The distance between the two points is about 628 m.
 Assignment: Practice Worksheet #3
 Unit 7 Test #2 Wednesday
• Sum and Difference Formulas
• Double Angle Formulas
• Half Angle Formulas
• Solve Trig Equations (includes factoring)
 Use remainder of class time to study for test
or work on Law of Sines and Law of Cosines.
```