To solve the triangle completely, we need to find the remaining angles (B and C) and the remaining side (c).
Since triangle ABC is a triangle, the sum of the angles must be equal to 180 degrees. Therefore, to find angle B, we will subtract angles A and C from 180 degrees.
Angle B = 180 degrees - (Angle A + Angle C)
Angle B = 180 degrees - (115 degrees + Angle C)
Angle B = 180 degrees - 115 degrees - Angle C
Now, we are given that Angle A = 115 degrees, so substituting that value, we have:
Angle B = 180 degrees - 115 degrees - Angle C
Angle B = 65 degrees - Angle C
Next, we can use the Law of Sines to find angle C:
sin C / c = sin B / b
We are given that angle B = 65 degrees, side b = 32 m. Substituting these values, we get:
sin C / c = sin 65 / 32
To find angle C, we can rearrange the equation:
sin C = (sin 65 / 32) * c
Now, we can find angle C using the inverse sine function:
C = sin^(-1)((sin 65 / 32) * c)
Next, we can find the remaining side c using the Law of Sines:
sin A / a = sin C / c
We are given that angle A = 115 degrees and side a is not known. Substituting these values, we have:
sin 115 / a = sin C / c
Since we have already found angle C, we can substitute that value:
sin 115 / a = sin(C) / c
To find side a, we can rearrange the equation:
a = (sin 115 / sin C) * c
Now that we have all the angles and sides, we have fully solved the triangle.