The Law of Cosines with an application problem.

1. 6.2: Law of
Cosines
Objective: Use the law of Cosines to solve oblique
triangles and find area.
Standard: Trigonometry 13.0, 14.0
Mr. Fjelstrom
1/13-14/11

2. The SSS and SAS cases can be solved using the …
Law of Cosines
Standard Form Alternative Form
In general:
opp2 = adj 2 + adj 2 − 2(adj)(adj) cos(Angle)
2

3. Example 1:
Find the three angles of the triangle.
SSS C
117.3°
6 8
36.3° 26.4°
A B
12
Find the angle
opposite the longest
side first.
Law of Sines:
3

4. Example 2:
C
Solve the triangle.
SAS 9.9
67.8° 6.2
Law of Cosines: 37.2° 75°
A 9.5
B
Law of Sines:
4

5. Heron’s Area Formula
Given any triangle with sides of lengths a, b, and c, the
area of the triangle is given by:
Example 3:
8 10
Find the area of the triangle.
5
5

6. Application:
Two ships leave a port at 9 A.M. One travels at a bearing of N
53° W at 12 mph, and the other travels at a bearing of S 67° W at
16 mph. How far apart will the ships be at noon?
N
At noon, the ships have traveled for 3 hours. 36 mi
43 m
i 53°
c
Angle C = 180° – 53° – 67° = 60° 60° P
67°
48 mi
The ships will be approximately 43 miles apart.
6

7. Homework:
#3 Law of Cosines WS (odd
problems)
#4 p. 437 #35, 36, 39, 40, 42
and p. 444 #32, 34, 35, 36, 41