Final answer:
The question is about converting polar coordinates to Cartesian coordinates and calculating the distance between points in the Cartesian coordinate system using appropriate mathematical formulas.
Step-by-step explanation:
The student's question concerns the conversion of polar coordinates to Cartesian coordinates and the calculation of distances between points in the Cartesian coordinate system. Polar coordinates describe a point's location based on a distance from the origin and an angle from the reference direction, whereas Cartesian coordinates define points based on their distance along perpendicular axes from the origin.
To convert from polar to Cartesian coordinates, we apply the following relationships: x = r*cos(θ) and y = r*sin(θ), where r is the radial distance and θ is the angle in radians. For distances between points in Cartesian coordinates, we employ the distance formula d = √((x2 - x1)² + (y2 - y1)²).
For example, to find the Cartesian coordinates for polar coordinates (2.500 m, π/6), we calculate x = 2.500 * cos(π/6) and y = 2.500 * sin(π/6). We perform a similar calculation for the second point and then apply the distance formula to determine the distance between them.