Let's analyze the given problem based on the uploaded image.

You have a triangle $\triangle XYZ$, with the following details:

• $XZ = 15 \, \text{cm}$
• $WX = 8 \, \text{cm}$ (marked as a perpendicular height from $W$ to $XY$)
• $\angle ZWY = 50^\circ$
• We need to find $\angle YXZ$, expressed to 1 decimal place.

This diagram involves two right-angled triangles: $\triangle WXY$ and $\triangle XYZ$. Let's proceed step by step.

Step 1: Use Right Triangle Properties in $\triangle WXY$

1. In $\triangle WXY$, since $WX$ is perpendicular to $XY$, we can use trigonometry.

   From the given:

   • $WX = 8 \, \text{cm}$
   • $\angle ZWY = 50^\circ$

   Use trigonometric ratios (tangent) to find side $WZ$: $\tan(50^\circ) = \frac{WX}{WZ}$ Rearranging: $WZ = \frac{8}{\tan(50^\circ)}$ Using $\tan(50^\circ) \approx 1.1918$: $WZ \approx \frac{8}{1.1918} \approx 6.71 \, \text{cm}$

Step 2: Find $\angle YXZ$

Now, we need to calculate $\angle YXZ$ (the angle at vertex $X$).

Notice that we are working with two triangles— the larger triangle $\triangle XYZ$ and the smaller right-angled triangle $\triangle WXY$. Specifically, the angle at $X$ can be calculated using trigonometry in the right triangle $\triangle XYZ$.

We can define the correct cos.