Final answer:
To find the measure of each side of the triangle ABC, use the distance formula to calculate the length of AB, BC, and AC. The length of AB is approximately 8.06 units, BC is approximately 9.22 units, and AC is approximately 11.40 units.
Step-by-step explanation:
To find the measure of each side of the triangle ABC, we can use the distance formula. The distance formula is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
Using the coordinates of the vertices A(-1,5), B(6, 1), and C(2,-6), we can find the length of each side:
AB = √[(6 - (-1))² + (1 - 5)²]
BC = √[(2 - 6)² + (-6 - 1)²]
AC = √[(-1 - 2)² + (5 - (-6))²]
Calculating these values, we get:
AB = √[(7)² + (-4)²]
BC = √[(-4)² + (-7)²]
AC = √[(-3)² + (11)²]
Simplifying further, we get:
AB ≈ 8.06 units
BC ≈ 9.22 units
AC ≈ 11.40 units