1. T4.1d To Use the Law of Cosines
Got ID?
Please get the two handouts from the table by the door.
Opener (Group activity):
DEAL OR NO DEAL?
I am being offered a terrific deal on a triangular piece of land, just $100 an acre! I was told that the angle at the lake is 109°, the side opposite the angle is 500 ft. long and the adjacent side is 600 ft. long. In paragraph form, explain WHY I should or should not take the deal. Although you may want to solve the triangle first, EXPLAIN YOUR PROCESS. Turn in one sheet of paper with all your FIRST & LAST names on it. However, I must see that you are all actively involved or your grade will be reduced. Please turn in your paper when the timer goes off. (43,560 ft2 / acre)

2. Active Learning Assignment Questions?

3. * * SAS LESSON: The Law of Cosines Geometric relationship?
If we want to find side a: * B
SAS c a
What if we want to find side b: C A b
Geometric relationship?
What if we want to find side c:
How is this different from the Law of Sines? *

4. First, should we try to use the Law of Sines? Why or why not?
Let’s try a simple example. We will find the length of the side labeled x, given the following measures (1 dec. pl.):
First, should we try to use the Law of Sines? Why or why not?
17 in. x
Now, re-write the formula:
31°
22 in.
Fill in the formula:
Don’t copy, just watch:
The length of x is 11.5 in.

5. Fill in the formula to find the red line:
#2: A parallelogram has a 70° angle and sides 6 cm and 10cm long. How long are its diagonals? (1 dec. pl.)
Fill in the formula to find the red line: 10
110°
70° 6 6
110°
70° 10
And now, the blue line:
***THE DIAGONAL DOES NOT BISECT THE ANGLE***
The diagonals are 9.7 cm and 13.3 cm.
***Future use?***

6. The distance between Matt City and Allyburg is 215 miles.
Try: Matt City and Allyburg are on opposite sides of the state, on an east-west line. A third city, Doodleville, is located between them, just a little to the north. The distance between Matt City and Doodleville is 120 miles, the distance between Doodleville and Allyburg is 150 miles, and the angle at Doodleville is 105°. Find the distance, to the nearest mile, between Matt City and Allyburg.
Fill in the formula: A M D
120
150
105° ?
The distance between Matt City and Allyburg is 215 miles.

7. * The Law of Cosines SSS! If we want to find side a, we use: B C a b c
Suppose we know a, b, & c, but want to find angle A. Your mission: Solve for angle A (get it by itself)
Now what?
(Subtract b2 and c2 from both sides)
(Take the arccosine of each side.)
And we have: *
SSS!
(Divided both sides by -2bc)
(The book uses another formula)

8. The angle at Solange’s houseboat is 111.8°.
Try: Jean Pierre and René live on opposite sides of Blue Bayou. Solange lives on her houseboat, moored between them, just a little to the north. If the distances between them are as shown in the diagram, find the angle at Solange’s houseboat. (1 dec. pl.) R J S
5 mi.
7 mi.
10 mi.
The angle at Solange’s houseboat is 111.8°.

9. Active Learning Assignment:
Law of Cosines Story Problems Handout (Answers on the handout): , 26, 27, 28, 32
II. Writing: “I do my best when I …”
WOW:
People don’t do the right thing because it is easy. They do it because, in spite of NOT being easy, It Is The Right Thing To Do!