Explain how you would solve a triangle given two sides and the included angle.
To solve a triangle given two sides and the included angle, you can use the Law of Sines.
1. Start by labeling the given information - the two sides and the included angle.
2. Use the Law of Sines, which states:
a / sin A = b / sin B = c / sin C
where a, b, and c are the sides of the triangle, and A, B, and C are the angles opposite those sides.
3. Plug in the given information into the formula. For example, if sides a and b are given, and angle A is the included angle, you can set up the equation as:
a / sin A = b / sin B
4. Solve for the unknown angle (angle B) by rearranging the formula and calculating sin B. Then, find the third unknown angle (angle C) by subtracting angles A and B from 180 degrees.
5. Finally, use the Law of Sines again to find the remaining side length. Plug in the known side lengths and angles into the formula and solve for the remaining side.
By following these steps, you can solve a triangle given two sides and the included angle.