Final answer:
To calculate the distance AC, the Pythagorean Theorem is applied to the right-angled triangle formed by the positions of A, B, and C. The distance is found to be 12.42km after solving the equation AC² = 8km² + 9.5km².
Step-by-step explanation:
The student's question addresses a problem in geometry, where they need to calculate the distance between two points labeled A and C, given that A is located 8km north of phone mast B and C is 9.5km west of phone mast B. This scenario can be visualized as a right-angled triangle, where A and C are the points defining the hypotenuse of the triangle, with B being the point where the two perpendicular sides measuring 8km and 9.5km meet.
To find the distance AC, we can apply the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Algebraically, this is represented by the equation c² = a² + b².
By plugging in the known values, we get:
AC² = 8km² + 9.5km²
AC² = 64 + 90.25
AC² = 154.25
Therefore, AC = √154.25
AC = 12.42km (rounded to two decimal places)
The distance AC is 12.42km, which is the direct distance between points A and C.