First, we should assign an angle to each side. *A*, *B*, and *C* will be the angles opposite the sides in *increasing* order. That means *a* = 10, *b* = 11, and *c* = 12. We'll find *A* first. *a*^{2} = *b*^{2} + *c*^{2} – 2*bc* cos *A*
To minimize confusion, we'll rearrange the equation before plugging things in. Wonderful. Now we're ready to plug in our sides. Our calculator can handle the rest. *A* ≈ 51.3°
Noice. Now we have an angle-side ratio, so we'll make use of the Law of Sines for the rest. We just calculated *A* and we want to calculate *B*. Rearrange the equation to solve for *B*. Calculate the angle. *B* ≈ 59.1°
Sweet. Two down, one to go. *A* + *B* + *C* = 180° 51.3° + 59.1° + *C* = 180°
For the last angle, we get: *C* = 69.6°
That means the angles of the triangle are 51.3°, 59.1°, and 69.6°. |