https://file.aiquickdraw.com/mathbot/file/1725829101728xc6gkl8k.jpg

The problem shows a triangle defined by three points:

- \( A = (1, 3) \)
- \( B = (6, 6) \)
- \( C = (10, 5) \)

We are asked to determine all three angles of the triangle in radians. The image provides these values:

- \( \theta_A = 0.4636 \, \text{radians} \)
- \( \theta_B = 0.3217 \, \text{radians} \)
- \( \theta_C = 2.3562 \, \text{radians} \)

To solve this type of problem, the general approach is to:
1. Calculate the lengths of the sides of the triangle using the distance formula between points.
2. Apply the Law of Cosines to find the angles.

Do you want a detailed step-by-step breakdown of how these angles were calculated or any additional clarifications? 

Here are five related questions:
1. How do you apply the Law of Cosines to find the angles in a triangle?
2. Can the sum of the angles in a triangle in radians exceed \( \pi \) (3.14159)?
3. How do you convert angles from radians to degrees?
4. What is the geometric significance of an angle larger than \( \pi/2 \) (right angle) in a triangle?
5. How can the Law of Sines be used to solve for angles in a triangle?

**Tip:** The sum of all interior angles in any triangle is always \( \pi \) radians (180 degrees).

A triangle is defined by three points: A = (1, 3), B = (6, 6), and C = (10, 5). Determine all three angles in radians, where θ_A = 0.4636 radians, θ_B = 0.3217 radians, and θ_C = 2.3562 radians.

Determine the angles of a triangle defined by points A(1, 3), B(6, 6), and C(10, 5) using trigonometry. Learn how to apply the distance formula and Law of Cosines to solve for angles in radians. Suitable for high school students in Grades 9-12.

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