Final answer:
To find the angles of the triangle, we can use the cosine rule and the Euclidean distance formula to calculate the lengths of the sides. We can then use the inverse cosine function to find the angles. The angles are A, B, and C.
Step-by-step explanation:
To find the angles of the triangle, we can use the cosine rule.
Let A = (4,1,-3), B = (2,1,0), and C = (0,1,6) be the vertices of the triangle.
Using the Euclidean distance formula, we find the lengths of the sides of the triangle: AB = √(2^2 + 3^2 + 3^2) = √22, BC = √(2^2 + 0^2 + 6^2) = 2√10, and AC = √(4^2 + 0^2 + 9^2) = √97.
By the cosine rule, the cosines of the angles are given by:
cos A = (BC^2 + AC^2 - AB^2) / (2 * BC * AC)
cos B = (AC^2 + AB^2 - BC^2) / (2 * AC * AB)
cos C = (AB^2 + BC^2 - AC^2) / (2 * AB * BC)
Substituting the values, we have cos A = 17 / (2√10 * √97), cos B = 1 / (2√10), and cos C = 81 / (2 * √10 * √97).
To find the angles, we can use the inverse cosine function:
Angle A = arccos(cos A), Angle B = arccos(cos B), and Angle C = arccos(cos C).
Learn more about Triangle Angles