The image contains 8 triangles, each with given sides and/or angles. These are most likely problems involving the Law of Cosines or Law of Sines, commonly used in trigonometry to find missing sides or angles in triangles.

Let's break down the given problems:

1. Triangle 1:

   • Sides: $AB = 6.7 \, \text{m}, AC = 8.6 \, \text{m}, BC = 13.7 \, \text{m}$
   • Likely requires the use of the Law of Cosines or Heron’s formula (for area).

2. Triangle 2:

   • Sides: $AB = 8 \, \text{mi}, AC = 10 \, \text{mi}$
   • Angle: $\angle ACB = 143^\circ$
   • Use Law of Cosines to find the third side $BC$.

3. Triangle 3:

   • Sides: $AB = 11.8 \, \text{ft}, AC = 9 \, \text{ft}$
   • Angle: $\angle BAC = 43^\circ$
   • Law of Cosines can be used to find side $BC$.

4. Triangle 4:

   • Sides: $AB = 7 \, \text{m}, BC = 15 \, \text{m}, AC = 16 \, \text{m}$
   • This might require Law of Cosines to find an angle.

5. Triangle 5:

   • Sides: $AB = 7 \, \text{yd}, BC = 7.3 \, \text{yd}$
   • Angle: $\angle ACB = 149^\circ$
   • Law of Cosines can help determine side $AC$.

6. Triangle 6:

   • Sides: $AB = 11 \, \text{mi}, AC = 14 \, \text{mi}$
   • Angle: $\angle BAC = 120^\circ$
   • Use Law of Cosines to find side $BC$.

7. Triangle 7:

   • Sides: $AB = 13 \, \text{ft}, BC = 8 \, \text{ft}, AC = 15 \, \text{ft}$
   • This could involve Heron’s formula for area or verifying a right triangle using the Pythagorean theorem.

8. Triangle 8:

   • Sides: $AB = 6 \, \text{ft}, BC = 6 \, \text{ft}$
   • Angle: $\angle ACB = 147^\circ$
   • Use Law of Cosines to find side $AC$.

Would you like me to solve specific problems from this set? Feel free to ask for further details!

Related Questions:

1. How can we use the Law of Cosines to solve non-right triangles?
2. What is the Law of Sines, and how is it used in triangle problems?
3. How do you calculate the area of a triangle using Heron’s formula?
4. When should you apply the Law of Sines over the Law of Cosines?
5. What steps are involved in solving a triangle using a mix of angles and sides?

Tip:

For triangles with large or obtuse angles, the Law of Cosines is typically more efficient for finding missing sides or angles.