Final answer:
To classify the triangle with coordinates A(-5,3), B(-2,-4), and C(2,6) on a coordinate plane, use the distance formula to find the lengths of the sides and the Law of Cosines to find the measures of the angles. This triangle is classified as a scalene and acute triangle.
Step-by-step explanation:
A triangle can be classified by its sides and angles. To classify the triangle with coordinates A(-5,3), B(-2,-4), and C(2,6) on a coordinate plane, we need to find the lengths of the sides and the measures of the angles. Using the distance formula, we find that side AB has a length of approximately 7.81 units, side BC has a length of approximately 10.82 units, and side AC has a length of approximately 8.60 units. Next, we can find the measures of the angles by using the Law of Cosines. After calculating the angles, we can determine the classification of the triangle.
The lengths of the sides are approximately AB = 7.81, BC = 10.82, and AC = 8.60 units.
The measures of the angles are approximately ∠A ≈ 72.33 degrees, ∠B ≈ 50.14 degrees, and ∠C ≈ 57.53 degrees.
Based on the lengths of the sides and the measures of the angles, this triangle is classified as a scalene triangle because all three sides have different lengths and as an acute triangle because all three angles are less than 90 degrees.