Final answer:
To calculate the length of line segment BC in triangle ABC, apply the distance formula by finding the absolute differences in the x- and y-coordinates of points B and C, and use the Pythagorean theorem. The length of segment BC is 50 units.
Step-by-step explanation:
To find the length of line segment BC in triangle ABC with vertices at A(0, 0), B(48, 0), and C(0, 14), we can use the distance formula. Since points B and C lie on the Cartesian coordinates, we only need to consider the change in the x- and y-coordinates between these two points.
Point B has coordinates (48, 0) and point C has coordinates (0, 14). The change in x-coordinate (Δx) is 48 - 0 = 48, and the change in y-coordinate (Δy) is 0 - 14 = -14. However, since we are interested in the absolute difference, we take the positive values of these differences.
The length of line segment BC is the Euclidean distance between points B and C, calculated using the Pythagorean theorem: BC = √(Δx² + Δy²) = √(48² + 14²) = √(2304 + 196) = √(2500) = 50 units.
Therefore, the length of line segment BC in triangle ABC is 50 units.