We can use the Law of Sines to find the length of side AC:
a/sin(A) = b/sin(B) = c/sin(C)
We know the length of side AB, which is the base line, so we can use it as side c in the formula. We also know the measures of angles A and B, so we can substitute them into the formula:
AB/sin(B) = AC/sin(A)
Substituting the values:
1 mile/sin(58.1 degrees) = AC/sin(118.1 degrees)
Simplifying:
AC = (1 mile x sin(118.1 degrees)) / sin(58.1 degrees)
AC = 1.186 miles
Therefore, the distance across the canyon from A to C is approximately 1.186 miles. I believe that is the answer you were looking for… I apologize if it’s not.