Law of Cosines (SAS) Quesc: \( 0 / 1 \quad \) Penaltr: 0.5 off In \( \Delta V W X, v=42 \) inches, \( w=76 \) inches and \( \angle \mathrm{X}=126^{\circ} \). Find the length of \( x \), to the nearest inch.

To find the length of \( x \) in triangle \( \Delta V W X \) using the Law of Cosines, you can use the formula: \[ x^2 = v^2 + w^2 - 2vw \cdot \cos(\angle X) \] Substituting the values, we have: \[ x^2 = 42^2 + 76^2 - 2 \cdot 42 \cdot 76 \cdot \cos(126^{\circ}) \] Calculating it step-by-step: 1. Calculate \( 42^2 = 1764 \) 2. Calculate \( 76^2 = 5776 \) 3. Find \( 2 \cdot 42 \cdot 76 \): \( 2 \cdot 42 \cdot 76 = 6372 \) 4. Now, find \( \cos(126^{\circ}) \), which is approximately \( -0.8090 \): Therefore, \[ -2 \cdot 42 \cdot 76 \cdot \cos(126^{\circ}) \approx 6372 \cdot 0.8090 \approx 5154.788 \] 5. Plug in all the values: \[ x^2 = 1764 + 5776 + 5154.788 \approx 12694.788 \] 6. Finally, take the square root to find \( x \): \[ x \approx \sqrt{12694.788} \approx 112.7 \] Rounding to the nearest inch, the length of \( x \) is approximately \( 113 \) inches.