In triangle $△wxy$, side $y$ is $940$ inches, angle $\angle y$ is $100°$, and angle $\angle w$ is $38°$. Find the length of side $w$ to the nearest inch.

• A. $604$ inches
• B. $1512$ inches
• C. $1312$ inches
• D. $727$ inches

Answer: (C)

Verified step by step guidance

1. Identify the given elements in triangle \( \triangle wxy \): side \( y = 940 \) inches, angle \( \angle y = 100^\circ \), and angle \( \angle w = 38^\circ \).
2. Calculate the measure of the third angle \( \angle x \) using the triangle angle sum property: \( \angle x = 180^\circ - \angle y - \angle w = 180^\circ - 100^\circ - 38^\circ \).
3. Use the Law of Sines to relate the sides and angles: \[ \frac{w}{\sin(\angle y)} = \frac{y}{\sin(\angle x)} \]. Here, \( w \) is the side opposite \( \angle w \), and \( y \) is the side opposite \( \angle y \).
4. Rearrange the Law of Sines formula to solve for side \( w \): \[ w = y \times \frac{\sin(\angle w)}{\sin(\angle x)} \].
5. Substitute the known values of \( y \), \( \angle w \), and \( \angle x \) into the equation and compute the sine values to find the length of side \( w \). Round the result to the nearest inch.