Explain how you would solve a triangle given two sides and the included angle.

Answer 1

To solve a triangle given two sides and the included angle, you can use the Law of Cosines.

1. Start by labeling the triangle with the given information. Let's say side a is opposite the angle, side b is adjacent to the angle, and side c is the remaining side.

2. Use the Law of Cosines formula to find the length of the third side, c. The Law of Cosines states: c^2 = a^2 + b^2 - 2abcos(C), where C is the included angle.

3. Once you have found the length of side c, you can use trigonometric functions (sine, cosine, or tangent) to find the other angles in the triangle. For example, you can use the sine rule: sin(A)/a = sin(B)/b = sin(C)/c to find the other angles.

4. You can now find the remaining angle by subtracting the sum of the two known angles from 180 degrees.

5. Now you have solved the triangle and found all the angles and side lengths.