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)

Active Learning Assignment Questions?

* * 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? *

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.

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?***

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.

* 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)

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°.

Active Learning Assignment: Law of Cosines Story Problems Handout (Answers on the handout): 25, 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!