To determine the length of the third side of a triangle given two angles, we first need to calculate the third angle using the fact that the sum of the angles in a triangle is always 180 degrees.
Given:
- Angle 1 = 10°
- Angle 2 = 12°
Calculate the third angle: \[ \text{Angle 3} = 180° - (10° + 12°) = 180° - 22° = 158° \]
Now, we can use the Law of Sines to determine the side lengths, but we first need to clarify your problem regarding which lengths we have and which one we need to find. Typically we would have either the lengths of two sides and want to find the third side, or we might be given the lengths opposite the two angles.
If we assume that the lengths of the sides opposite the first two angles (10° and 12°) are known, please provide those lengths to proceed.
Without additional information on the lengths of sides opposite the given angles, we cannot conclusively determine the length of the third side. However, let's examine your responses:
- Side x equals 1 m: This could be a solution if the corresponding side fits the triangle inequality.
- Side x equals 2 m: Similarly, this could also be a candidate.
- Side x equals 13 m: This seems less likely without the context of the other sides, as it must still satisfy the triangle inequality (the sum of the lengths of any two sides must be greater than the length of the remaining side).
If you can provide more details about the sides or context of the problem, I can help further determine the correct side length.
1 answer