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round side measures to the nearest tenth and angle measures to the nearest degree

The image shows a right triangle \( \triangle WXZ \) with the following information provided:

- \( \angle X = 90^\circ \) (right angle),
- \( \angle Z = 57^\circ \),
- Side \( WZ = 18 \).

We need to find the lengths of sides \( WX \) and \( XZ \), and the measure of \( \angle W \). We'll use trigonometric functions to solve this.

### Step 1: Find \( \angle W \)
Since the sum of the angles in any triangle is \( 180^\circ \), we have:
\[
\angle W = 180^\circ - 90^\circ - 57^\circ = 33^\circ
\]

### Step 2: Find side \( XZ \) (opposite to \( \angle Z \))
Using the sine function:
\[
\sin(\angle Z) = \frac{XZ}{WZ}
\]
\[
XZ = WZ \times \sin(57^\circ) = 18 \times \sin(57^\circ)
\]
\[
XZ \approx 18 \times 0.8387 \approx 15.1
\]

### Step 3: Find side \( WX \) (adjacent to \( \angle Z \))
Using the cosine function:
\[
\cos(\angle Z) = \frac{WX}{WZ}
\]
\[
WX = WZ \times \cos(57^\circ) = 18 \times \cos(57^\circ)
\]
\[
WX \approx 18 \times 0.5446 \approx 9.8
\]

### Final Results
- \( \angle W \approx 33^\circ \)
- \( XZ \approx 15.1 \)
- \( WX \approx 9.8 \)

Let me know if you want

Round side measures to the nearest tenth and angle measures to the nearest degree for triangle WXZ where angle X is 90 degrees, angle Z is 57 degrees, and side WZ is 18.

Discover how to solve triangle WXZ by rounding side measures to the nearest tenth and angle measures to the nearest degree. This problem involves trigonometric functions such as sine and cosine to find missing side lengths and angles, suitable for students in Grades 9-10.

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