How to Find the Missing Degrees of a Triangle

Use a graphing calulator to help you find your math answers.

Math is one subject that many students are not always fond of. There is one important thing to remember about most types of maths: there is normally a specific equation that will help you find your answer. To find the degrees of a triangle, remember that the equation is A + B + C = 180. All of the interior degrees of the triangle have to add up to 180 degrees. It does, however, become a bit more tricky if only one degree is know, but the answer is still easy to find.

Things You'll Need

• Calculator

Instructions

1. Look at what information you have. If you need to find the missing interior degrees of a triangle, than the lengths of the exterior sides will be given to you. For this equation, let's say that Side a = 2, Side b = 3 and Side c = 4.

2. Know that it's always easiest to the find the largest degree, or angle, first because only that angle will be larger than 90 degrees. In this case, Side c is the largest at 4.

   To find the angle, use the cosine rule:
   c^2 = b^2 + a^2 - 2ba(cosC)

   Start by adding 2ba(cosC) to both sides to pull it to the left side of the equation. Subtract c^2 from both sides to pull it to the right side. Also, reverse b^2 with a^2 the letters are in numeric order:
   2ba(cosC) = a^2 + b^2 - c^2

   Divide 2ba from both sides to be able to solve for cosC on the left:
   cosC = a^2 + b^2 - c^2 / 2ab

   Plug in your numbers and solve:
   cosC = 2^2 + 3^2 - 4^2 / 2 x 2 x 3
   cosC = (2 x 2) + (3 x 3) - (4 x 4) / 2 x 2 x 3
   cosC = 4 + 9 - 16 / 12
   cosC = -3 / 12
   cosC = - 0.25

   Now find the inverse cos of -0.25 with your calculator:
   C = cos^-1 (-0.25)

   Angle C = 104.48 degrees

3. Determine what angle A is by using the exterior sides of the triangle, as well as known angle C (104.48).

   To find the angle, use the sine rule:
   a / sin A = c / sinC

   Multiply side a from both sides to solve for sinA. Then, reverse side c with sinC:
   sinA = a sinC / c

   Plug in your numbers to solve:
   sin A = 2sin104.48 / 4

   Type 104.48 into your calculator, followed by "sin" and solve:
   sin A = 2 x 0.967 / 4
   sin A = 1.934 / 4
   sin A = 0.484

   Now find the inverse sin of 0.484 with your calculator:
   A = sin^-1 (0.484)

   Angle A = 28.95 degrees

4. Find the last angle, angle B, by using the easier formula there is: the Sum of Internal Angles rule:
   A + B + C = 180.

   Subtract (A + C) from both sides to solve for B on the left side of the equation:
   B = 180 - (A + C)

   Plug in your known angles to find the remaining unknown degree:
   B = 180 - (28.95 + 104.48)
   B = 180 - 133.43
   B = 46.57

   Angle B = 46.57 degrees

References

• Math is Fun: Pythagorean Theorem
• Teacher's Choice: Trigonometry
• Math's Teacher: Angle Sum of a Triangle