To create a unique triangle given one side length and two angles, we can apply the Angle-Side-Angle (ASA) theorem. This theorem states that if two angles and the included side (the side between those angles) are known, then a unique triangle can be formed.

Explanation of the setup:

1. Side Length: You need to choose a side.
2. Two Angles: The sum of angles in any triangle is always 180°. So, once we select two angles, the third angle is automatically determined. The key is to ensure that the angles and side form a valid triangle configuration.

Example:

• Side Length (units): 5
• Angle 1 (degrees): 45°
• Angle 2 (degrees): 60°

Why does this form a unique triangle?

1. The sum of these two angles is $45^\circ + 60^\circ = 105^\circ$. Therefore, the third angle will be $180^\circ - 105^\circ = 75^\circ$.
2. Since we know two angles and the side between them (ASA), a unique triangle can be formed, as there is only one way to fit the given side length between those two angles.

Additional notes:

• The choice of side length and angles must be such that they form a valid triangle (sum of angles = 180°).
• Ensure that the side is between the two angles to guarantee uniqueness.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What is the Side-Angle-Side (SAS) theorem, and how does it differ from ASA?
2. Can we form a unique triangle if we are given two angles and a non-included side?
3. How would the solution change if we knew two sides and an angle (SSA case)?
4. What happens if we choose angles that are too large or too small?
5. How do we apply trigonometric functions to find other sides and angles of a triangle?

Tip: Always remember that the sum of interior angles in any triangle is $180^\circ$, which can help confirm if the triangle is valid!