Geometry 8-6a GeoGebra Primer: Law of Cosines
By Matt Richardson
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Last updated about 3 years ago
10 Questions
Interact with the embedded GeoGebra applet before responding to the items that follow.
Make sure that the black slider has been slid all the way to the right before responding to the questions.
10 points
10
Question 1
1.
Vocabulary: What is segment h?
Vocabulary: What is segment h?
10 points
10
The same applet is embedded multiple times throughout this activity for convenience as you respond to the items that follow.
10 points
10
Question 3
3.
Exploration: Write an equation that expresses the relationship among A, x, and b.
Exploration: Write an equation that expresses the relationship among A, x, and b.
10 points
10
Question 4
4.
Exploration: Rewrite the equation from the previous item so that x is in terms of A and b.
Exploration: Rewrite the equation from the previous item so that x is in terms of A and b.
10 points
10
Question 5
5.
Exploration: Write an equation that expresses the relationship among b, x, and h.
Exploration: Write an equation that expresses the relationship among b, x, and h.
10 points
10
Question 6
6.
Exploration: Without introducing a new variable, write an equation that expresses the relationship among the sides of △BDC.
Exploration: Without introducing a new variable, write an equation that expresses the relationship among the sides of △BDC.
Check-up: The expanded form of the equation you selected in the previous item looks like this.
If it does not, reconsider your selection.
10 points
10
Question 7
7.
Exploration: The expanded equation above can be re-written as follows.
Exploration: The expanded equation above can be re-written as follows.
Which property justifies this?
10 points
10
Question 8
8.
Exploration: The equation in the previous item can be re-written in this form.
Exploration: The equation in the previous item can be re-written in this form.
Which property justifies this?
10 points
10
Question 9
9.
Exploration: In item 4, you found that x = bcos(A). Therefore, the equation in the previous item can be written as follows.
Exploration: In item 4, you found that x = bcos(A). Therefore, the equation in the previous item can be written as follows.
In addition to the Commutative Property of Multiplication, which property justifies this?
10 points
10
Question 10
10.
Exploration: In item 5, you found that b² = h² + x². Therefore, the equation in the previous item can be written as follows.
Exploration: In item 5, you found that b² = h² + x². Therefore, the equation in the previous item can be written as follows.
Which property justifies this?
Discovery: This equation is one form of the Law of Cosines.
The Law of Cosines can be used to identify unknown parts of non-right triangles.
