To find $x$, we can apply the Law of Sines since we know two angles (26° and 31°) and the length of the side opposite the remaining angle (25 m). Here’s the step-by-step solution:

1. Calculate the third angle: $180^\circ - 26^\circ - 31^\circ = 123^\circ$ So, the angle opposite $x$ is 123°.

2. Set up the Law of Sines formula**: $\frac{x}{\sin(123^\circ)} = \frac{25}{\sin(31^\circ)}$

3. Solve for $x$: Rearrange to solve for $x$: $x = \frac{25 \cdot \sin(123^\circ)}{\sin(31^\circ)}$

4. Calculate the values:

   • $\sin(123^\circ) \approx 0.8387$
   • $\sin(31^\circ) \approx 0.5150$

   Substitute these values in: $x = \frac{25 \cdot 0.8387}{0.5150} \approx 40.74$

After calculating, the answer to two decimal places is: $x \approx 40.74 \, \text{m}$

Answer: None of the options provided (closest answer was likely missing from choices).

Would you like further clarification, or have any questions?

Related Questions:

1. How do we use the Law of Sines for a different type of triangle?
2. What if we know two sides and one non-included angle? How do we solve that?
3. How does the Law of Cosines differ in application from the Law of Sines?
4. What is the role of each angle’s sine value in determining side lengths?
5. Can we use trigonometric ratios for non-right triangles in all cases?

Tip:

Remember that the Law of Sines is especially useful when you know either two angles and a side (AAS or ASA) or two sides and a non-included angle (SSA).