Solve the triangle. \[ \mathrm{a}=96.0 \text { in., } \mathrm{b}=60.0 \text { in., } \mathrm{B}=25.0^{\circ} \] Select the correct choice below and fill in the answer boxes within the choice. (Round to the nearest tenth as needed.) A. There is only 1 possible solution for the triangle. The measurements for the remaining angles A and C and side c are as follows. \( A \approx \) \( \square \) \( C \approx \) \( \square \) \( { }^{\circ} \) \( \mathrm{c} \approx \) \( \square \) in. B. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. A \( \approx \) \( \square \) \( C \approx \) \( \square \) \( { }^{\circ} \) \( \mathrm{c} \approx \) \( \square \) in. The measurements for the solution with the shorter side c are as follows. \( A \approx \) \( \square \) \( { }^{\circ} \) \[ C \approx \] \( \square \) \( { }^{\circ} \) \( c \approx \) \( \square \) in. C. There are no possible solutions for this triangle.

To solve the triangle, we will employ the Law of Sines. With side a = 96.0 in, side b = 60.0 in, and angle B = 25.0°, we can first find angle A. Using the sine rule, we have: \[ \frac{a}{\sin A} = \frac{b}{\sin B} \] Plugging in the values, we can calculate angle A, and subsequently angle C using the fact that the sum of angles in a triangle equals 180°. After performing the calculations, we arrive at: A ≈ 57.8°, C ≈ 97.2°, and c ≈ 77.4 in. How cool is it that just with some basic knowledge of angles and sides, we can unlock the mysteries of triangles? It's like being a geometric detective! In addition, understanding triangles is more than just a math exercise; it's foundational to various real-world applications. Whether you're designing a building, creating a computer game, or mapping out a landscape, mastering triangle properties equips you to tackle complex structures and animations. Triangles ensure stability and aesthetics in design, and their principles are backing the technology we use every day!