Solve for either "x" or "θ" in each right triangle.

This image contains six separate right-angled triangles, each with some known side lengths and/or angles. The task is to solve for the unknown variable, either "x" (a side length) or "θ" (an angle), in each triangle. Since the triangles are not to scale, we must use trigonometric ratios (sine, cosine, tangent) and the Pythagorean theorem.

I will solve each triangle one by one, starting from the top-left and moving across the rows.

---

Triangle 1 (Top-Left)

- Given: A right-angled triangle with an adjacent side of 6, a hypotenuse of 11, and the angle θ between them.
- Find: Angle θ.
- Method: Use the cosine function, as cos(θ) = adjacent / hypotenuse.
- cos(θ) = 6 / 11
- θ = arccos(6/11)
- θ ≈ arccos(0.5455) ≈ 56.9°

---

Triangle 2 (Top-Middle)

- Given: A right-angled triangle with an opposite side of 9, an angle of 32°, and the hypotenuse labeled x.
- Find: Hypotenuse x.
- Method: Use the sine function, as sin(32°) = opposite / hypotenuse.
- sin(32°) = 9 / x
- x = 9 / sin(32°)
- x ≈ 9 / 0.5299 ≈ 17.0

---

Triangle 3 (Top-Right)

- Given: A right-angled triangle with an adjacent side of 9, a hypotenuse of 13, and the angle θ between them.
- Find: Angle θ.
- Method: Use the cosine function, as cos(θ) = adjacent / hypotenuse.
- cos(θ) = 9 / 13
- θ = arccos(9/13)
- θ ≈ arccos(0.6923) ≈ 46.2°

---

Triangle 4 (Bottom-Left)

- Given: A right-angled triangle with an opposite side of 7, an angle of 29°, and the hypotenuse labeled x.
- Find: Hypotenuse x.
- Method: Use the sine function, as sin(29°) = opposite / hypotenuse.
- sin(29°) = 7 / x
- x = 7 / sin(29°)
- x ≈ 7 / 0.4848 ≈ 14.4

---

Triangle 5 (Bottom-Middle)

- Given: A right-angled triangle with an adjacent side of 3, an opposite side of 6, and the angle θ at the vertex where the adjacent side meets the hypotenuse.
- Find: Angle θ.
- Method: Use the tangent function, as tan(θ) = opposite / adjacent.
- tan(θ) = 6 / 3 = 2
- θ = arctan(2)
- θ ≈ 63.4°

---

Triangle 6 (Bottom-Right)

- Given: A right-angled triangle with an adjacent side of 5, an angle of 48°, and the opposite side labeled x.
- Find: Opposite side x.
- Method: Use the tangent function, as tan(48°) = opposite / adjacent.
- tan(48°) = x / 5
- x = 5 * tan(48°)
- x ≈ 5 * 1.1106 ≈ 5.55

---

Final Answers:

1. Top-Left Triangle: θ ≈ 56.9°
2. Top-Middle Triangle: x ≈ 17.0
3. Top-Right Triangle: θ ≈ 46.2°
4. Bottom-Left Triangle: x ≈ 14.4
5. Bottom-Middle Triangle: θ ≈ 63.4°
6. Bottom-Right Triangle: x ≈ 5.55

These values are rounded to one decimal place for clarity.