How to Find Angle of Triangle

Math can be difficult for many people. Throw in angles, formulas, polygons, degrees, cosines, and it can certainly be a disaster (and seem a lot more like science than math). Finding an angle of a triangle can be easy as long as you know the correct formula. "Triangle" refers to any polygon, or closed-plane shape, with three sides. Once you find the first angle, finding the other two is a piece of pi--er, cake.

Things You'll Need

• Calculator

Instructions

1. Remember that all of the angles will equal 180 degrees. The lengths of the sides of the triangle will always be given (you can't find the angles without them).

   For example: You have angles A, B and C, C being the largest angle (you always want to find the largest angle first), and you have three sides of the triangle a, b, and c. Let's say a = 2, b = 3, and c = 4.

2. Find C first.
   Find the largest angle with this formula:
   c squared = b squared + a squared - 2ba cosC

   Plug in the numbers we do have:
   4 squared = 3 squared + 2 squared - 2(3)(2) cosC

   Now, divide both sides by cosC and subtract 4 squared:
   cosC = 3 squared + 2 squared - 4 squared / 2x3x2

   Now, multiply the squares:
   cosC = 9 + 4 - 16 / 12

   Finish the math on the left:
   cosC = 13 - 16 / 12
   cosC = -3 / 12
   cosC = -0.25

   The inverse cos of -0.25 (you can find this right on your calculator) is 104.478
   cos C = 104.478

3. Find A next.
   The angle A using the sin rule:

   a / sinA = c / sinC

   Multiply both sides by a, so get sinA by itself. Then switch c and sinC:
   sinA = a (sinC) / c

   Plug in your numbers:
   sinA = 2 (sin 104.478) / 4

   Plug those numbers into your calculator and you get:
   sinA = 0.484123

   The inverse of 0.484123 is 28.955
   Therefore, angle A = 28.955

4. Find angle B last.
   Now that you have the other two angles (A = 28.955; C = 104.478), you can easily find B using this formula:
   A + B + C = 180

   Plug in our numbers:
   28.955 + B + 104.478 = 180.

   Subtract 28.955 and 104.478 to isolate B:
   B = 180 - (28.955 + 104.478)

   Always work inside the parentheses first:
   B = 180 - (133.433)

   Subtract to find out what B is:
   B = 46.5675

5. Write down your answer:

   Angle A = 28.955
   Angle B = 46.5675
   Angle C = 104.478

References

• Teachers Choice: Solve Triangle