SOLUTION: LAW OF COSINE?? Let the angles of a triangle be alpha, beta, and gamma, with opposite sides of length a, b, and c, respectively. Use the Law of Cosines to find the remaining sid

Algebra ->  Trigonometry-basics -> SOLUTION: LAW OF COSINE?? Let the angles of a triangle be alpha, beta, and gamma, with opposite sides of length a, b, and c, respectively. Use the Law of Cosines to find the remaining sid      Log On


   

Question 811744: LAW OF COSINE??
Let the angles of a triangle be alpha, beta, and gamma, with opposite sides of length a, b, and c, respectively. Use the Law of Cosines to find the remaining side and one of the other angles.
alpha = 46 degrees b = 10 c = 18

I get that there is a formula but I am having so many issues with putting it into my TI-84 calculator!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the law of cosines is
a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28alpha%29
and that would allow you to calculate a .
With any scientific calculator you could enter the formula
a=sqrt%28b%5E2%2Bc%5E2-2%2Ab%2Ab%2Acos%28alpha%29%29
In your case,
a=sqrt%2810%5E2%2B18%5E2-2%2A10%2A18%2Acos%2846%5Eo%29%29
With a simpler scientific calculator, I can do that calculation several ways.
The TI-84 is just a bit more complicated.

It is important to make sure that you are set to calculate trigonometric functions with the angle measured in degrees.
The more complicated the calculator, the harder it is to set it to use degrees.
You may have to go to the manual to figure out how to set the "MODE" to degrees.
Maybe pressing MODE you will get a menu and will have to choose from the menu by using arrow keys and hitting ENTER when degrees is highlighted.

With my calculator in degree mode, I can key in
10 x%5E2 + 18 x%5E2 - 2 times 10 times 18 times 46 cos
after that I press = to calculate 10%5E2%2B18%5E2-2%2A10%2A18%2Acos%2846%5Eo%29 ,
but you probably have to press ENTER instead of = ,
and you probably have to press highlight%28%22cos%22%29 46 highlight%28%22%29%22%29 instead of 46 cos.
Then, I press shift x%5E2 to get the square root,
but you must have to press the blue key instead of shift.

Once you have a and alpha , law of sines lets you get the rest easily.