In ΔXYZ, ∠Y=90° and ∠X=14°. ∠ZWY=50° and XW=40. Find the length of ZY to the nearest integer. 


To solve this problem, let's break it down carefully using the given information:

1. **ΔXYZ** is a right triangle with ∠Y = 90° and ∠X = 14°.
2. There is an additional angle ∠ZWY = 50°, and we are given that \( XW = 40 \) units.
3. We need to find the length of side \( ZY \) to the nearest integer.

### Step-by-Step Breakdown:

#### 1. **Find ∠Z:**
Since the sum of angles in any triangle equals 180°, we can find ∠Z in triangle XYZ:
\[
∠Z = 180° - ∠X - ∠Y
\]
\[
∠Z = 180° - 14° - 90° = 76°
\]

#### 2. **Apply the Law of Sines:**
Using the Law of Sines in triangle XYZ:
\[
\frac{ZY}{\sin(X)} = \frac{XZ}{\sin(Y)} = \frac{XY}{\sin(Z)}
\]
Since ∠Y = 90°, we can simplify this. But first, we need to apply trigonometric rules to use the correct formula.

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In ΔXYZ, ∠Y=90° and ∠X=14°. ∠ZWY=50° and XW=40. Find the length of ZY to the nearest integer.

Solve the problem of finding the length of side ZY in a right triangle ΔXYZ, where ∠Y = 90°, ∠X = 14°, and ∠ZWY = 50°. Learn how to apply the angle sum property and the Law of Sines to find the solution. Suitable for students in Grades 10-12.

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