https://file.aiquickdraw.com/mathbot/file/1730122463887ve16qalq.jpg

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.

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### **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 \( \tan(50^\circ) \approx 1.1918 \):
   \[
   WZ \approx \frac{8}{1.1918} \approx 6.71 \, \text{cm}
   \]

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### **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.

Find the angle ∠YXZ in the given triangle XYZ with XZ = 15 cm, WX = 8 cm, and ∠ZWY = 50°.

Learn how to find the angle ∠YXZ in triangle XYZ with given measurements XZ = 15 cm, WX = 8 cm, and ∠ZWY = 50°. This solution uses trigonometric ratios to calculate the missing angle, suitable for students in Grades 9-11.

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