Part 1- Dear Marty Mart Mart
The Law of Sines and the Law of Cosines are very helpful in solving triangles that don’t have a right or 90° angle. The law of sines is a/Sin A= b/ Sin B= c/ Sin C. A triangle looks like this:
You use ratios to solve for the unknown. If you have at least one matched pair (for example an A and an a) you can use the law of sines. If A= 26 and a= 14 and B=100 you would set the equation up like this: 14/Sin 26= b/Sin 100 you would then take (Sin100 *14)/Sin26=b. The law of Cosines is a^2= b^2+ c^2 -2 bc Sin A or solved for c or b. If you are solving for those it is always the Sin of that big letter and the other two little letters squared. Using the numbers a= 14, b= 26 and c= 29 the Law of Cosines would be: 14^2= 26^2 + 29^2 – 2*26*29*Cos A. This would give you angle A. You can manipulate the formula to solve for any of the unknown factors.
Now about your area problem. There basically is only 2 area formulas. The first one is the basic A= 1/2bh. The sin and cos and are in the formula so that way you can solve for the height of the triangle. To find the height you draw in a right triangle within the other triangle. then you use sin or cos to find the side length. You then take that and multiply it by the base and divide by 2. The equation is different because it includes the sin into the equation. The other Area formula is A= √(s(s-a)(s-b)(s-c)). This is called Heron’s formula. It uses the side lengths to find the area without worrying about finding the height.
Part 2
First you would solve for C. You take 180 – (A+ B) = C. C= 79 degrees. Then you can use the law of Sines to solve for a or b. 12/ Sin 79= a / Sin75. a=11.808. You then do the same thing for b. 12/ Sin79= b/Sin 26. b= 5.358.
Part 3
you could use the law of sines to find the how long the sides of this piece of pizza are. =]
Or use it for this bike seat.. no wonder they’re so uncomfortable…
You could use sin or cos to figure out the sides of a dorito =]
Part 4
you might be in pre- calc if you understand how to do Trig but are losing touch with basic math like addition and subtraction.
