I haven’t forgotten about my pledge to focus more content here towards some of the areas I’ve been asked to tutor on recently. This latest one is designed to help users understand the properties of triangles. It is based on two laws that we learn in trigonometry: the law of sines and the law of cosines. Assume that we have a triangle with sides of lengths a, b, and c and respective angles A, B and C (where the angle A does not touch the side a, the angle B does not touch the side b, and the angle C does not touch the side c). These laws are as stated as follows:
Law of Sines

= 

= 

Law of Cosines
c^{2} = a^{2} + b^{2} – 2*a*b*cos(C)
We can use these laws to determine the sides of a triangle given almost any combination of sides and angles of that triangle (the only one we cannot determine properties from is if we are given all three angles, as this leads to many solutions).
The script generates random triangles, with different combinations of sides and angles revealed and the user’s job is to try to determine the missing sides. There is a button to reveal the solution, or if you’d like to see how we arrive at these values, you can check the “Show work” box.
Hope you enjoy.
Other Blogs covering this topic:
Mathematical!
Algebra 2 Trig
 Triangle Sum Puzzle (0.800)
 Learn Duality in Linear Programming (0.330)
 The PageRank Algorithm (0.330)
 Learn Math Through Set Relations (0.295)
 How Could You Possibly Love/Hate Math? (0.275)
Besides your having the law of cosines wrong, an interesting challenge is to see how far students go before they (hopefully) see the issue when you give them a = 3, b = 4 and c = 7 and ask them to find angle C.
Thanks for noticing that. That’s one problem with edit replace – its easy to repeat mistakes. I’ve gone through and made the corrections though.
What a nice collection of algorithms, problems, explanations, …! It’s addictive and instructive.
Dr. Dean,
I appreciate you coming to take a look at my site as well as your words of encouragement. Words like “addictive and instructive” are exactly what I hoped to hear when I began putting this site together. Let me know if there are any additional concepts you’d like to see included.