Short Answer 
The analysis involves recognizing a right triangle formed by streets, where the opposite side (AC) is 21 miles. Using the tangent ratio (Tan(x) = Opposite / Adjacent) with a tangent value of 7/5, the length of the adjacent side (AB) is calculated to be 15 miles, confirming the distance between First Street and Oak Street as 15 miles.
Step 1: Analyze the Geometry
Begin by examining the layout of the streets to understand the relationship between First Street and Oak Street. Notice that lines AC and AB form a right triangle, where angle A is a right angle (90 degrees). The three sides of this triangle consist of:
- AC (opposite side) = 21 miles
- AB (adjacent side) = unknown length
- BC (hypotenuse) = y miles
Step 2: Apply the Tangent Ratio
To find the length of AB, use the tangent trigonometric ratio that relates the opposite side to the adjacent side in a right triangle. The formula is:
- Tan(x) = Opposite / Adjacent
- This translates to: Tan(x) = AC / AB, or Tan(x) = 21 / AB
- From the problem, the tangent value has been determined as 7/5, leading to the equation: 1.4 = 21 / AB
Step 3: Calculate the Length of AB
Rearranging the equation from Step 2 allows determination of AB. By multiplying both sides by AB and then excluding AB from the denominator, you derive:
- AB = 21 / 1.4
- AB = 15 miles
Thus, the distance between First Street and Oak Street is confirmed to be 15 miles.