Time Allotment: 5 minutes
Students will use Law of Sines Proof - Geogebra worksheet to review the proof of the Law of Sines. The teacher will circulate around the room as students work through the proof.
Note: This activity can be done as a whole class activity with the worksheet being projected on the board.
1. Give student pairs a copy of the Area of a Triangle activity. Ask them to complete problems 1-2.
2. Problems 1-2 require students to find the area of triangles given the values of the base and the height. Students will use the formula A=1/2 base x height. Check student work and clear up misconceptions.
3. Next, ask students to complete problems 3-4. These problems do not have a value for the height. The measure of angle A is provided and students will have to use the relationship Sine A = Opposite side (height)/ Hypotenuse (side C). Let students try to solve this problem on their own. If a pair of students do not recognize that they need to use a right triangle relationship lead them to this discovery with questioning.
4. Finally, ask students to complete problem 5. In this problem there are no numerical values given. This problem should lead them to discover that there is a formula for finding the area when given 2 sides and the included angle. Again, circulate among the groups to provide guidance when needed.
5. Allow students to share the formulas they found with the class. Be sure that the entire class can see where the formula for the area comes from. Also be sure that the class is aware that there is more than one way to write the formula based on what is given. The formulas are Area= (1/2)b*c*SinA=(1/2)a*c*SinB=(1/2)a*b*SinC
6. Assign practice problems and allow students to find the area of a triangle using the formula.
Check the answers to the practice problems. Ask students to write a note to a student who might have missed the lesson today. They should explain in detail and in their own words how to find the area of a triangle when two sides and the included angle are given. Tell them that writing the formula will not be enough. They need to explain the formula. Collect these and use this as your exit slip.