A. Solve each of the following triangles by first determining whether you can use Law of Sines or Law of Cosines. **When you have the ambiguous case, do not forget to find all possible triangles. Please round all angles to the nearest 10th and all sides to the nearest 100th. B. Make a sketch of each triangle solution, label all angles and side lengths on the triangle. You do not need to draw them exactly, but they should be representative of the actual triangles. C. Find the area of each triangle you found in part A using either the standard area formula or Heron's Formula. 1. Solve triangle ABC if C =14.5°, b=10, c= 4

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### Solving Triangles Using the Law of Sines and Cosines

**A. Problem-Solving Steps:**

1. Solve each of the following triangles by first determining whether you can use the Law of Sines or the Law of Cosines. 
   - **Note:** In cases where the solution is ambiguous, ensure that you find all possible triangles. 
   - Round all angles to the nearest tenth and all sides to the nearest hundredth.

**B. Visual Representation:**

1. Create a sketch for each triangle solution. 
   - Label all angles and side lengths on the triangle.
   - Exact proportions are not required, but the sketches should accurately represent the triangles.

**C. Area Calculation:**

1. Determine the area of each triangle found in Part A using either the standard area formula or Heron’s Formula.

---

### Problems:

1. **Solve Triangle ABC:**
   - Angle \( C = 14.5^\circ \)
   - Side \( b = 10 \)
   - Side \( c = 4 \)

2. **Solve Triangle ABC:**
   - Side \( a = 32 \)
   - Side \( b = 20 \)
   - Side \( c = 40 \)
Transcribed Image Text:### Solving Triangles Using the Law of Sines and Cosines **A. Problem-Solving Steps:** 1. Solve each of the following triangles by first determining whether you can use the Law of Sines or the Law of Cosines. - **Note:** In cases where the solution is ambiguous, ensure that you find all possible triangles. - Round all angles to the nearest tenth and all sides to the nearest hundredth. **B. Visual Representation:** 1. Create a sketch for each triangle solution. - Label all angles and side lengths on the triangle. - Exact proportions are not required, but the sketches should accurately represent the triangles. **C. Area Calculation:** 1. Determine the area of each triangle found in Part A using either the standard area formula or Heron’s Formula. --- ### Problems: 1. **Solve Triangle ABC:** - Angle \( C = 14.5^\circ \) - Side \( b = 10 \) - Side \( c = 4 \) 2. **Solve Triangle ABC:** - Side \( a = 32 \) - Side \( b = 20 \) - Side \( c = 40 \)
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