Question

To determine the distance across the Grand Canyon in Arizona, a 1 mile base line, call it AB or side c, is established along the southern rim of the canyon. Sightings are then made from points A & B to a point C across the canyon. Find the distance across the canyon from A to C if ∠BAC is 118.1 degrees and ∠ABC = 58.1 degrees.

Answer 1

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.