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Let's go through each problem step-by-step to find the required values for \( x \). I'll calculate the unknown sides and angles using trigonometric rules, mainly the Sine Rule and the Cosine Rule.

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### First Image

#### 1. Top Left Triangle:
- **Given**:
  - \( \angle 84^\circ \) and \( \angle 32^\circ \) in a triangle.
  - Side opposite \( \angle 32^\circ \) is \( 5.8 \) cm.

- **Find \( x \)** (side opposite \( \angle 84^\circ \)).

Using the Sine Rule:
\[
\frac{x}{\sin(84^\circ)} = \frac{5.8}{\sin(32^\circ)}
\]
Solving for \( x \):
\[
x = \frac{5.8 \times \sin(84^\circ)}{\sin(32^\circ)}
\]

#### 2. Top Right Triangle:
- **Given**:
  - \( \angle 80^\circ \) and \( \angle 67^\circ \).
  - Side opposite \( \angle 67^\circ \) is \( 7.4 \) cm.

- **Find \( x \)** (side opposite \( \angle 80^\circ \)).

Using the Sine Rule:
\[
\frac{x}{\sin(80^\circ)} = \frac{7.4}{\sin(67^\circ)}
\]
Solving for \( x \):
\[
x = \frac{7.4 \times \sin(80^\circ)}{\sin(67^\circ)}
\]

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### Second Image

#### 3. Bottom Left Triangle:
- **Given**:
  - Side lengths \( 6 \) cm and \( 4.6 \) cm.
  - Angle \( 44^\circ \).

- **Find \( x \)** (unknown angle).

Using the Cosine Rule to find \( x \):
\[
x = \cos^{-1}\left(\frac{6^2 + 4.6^2 - c^2}{2 \times 6 \times 4.6

Find the unknown sides and angles in each triangle given in the images using trigonometric rules. Give your answers to the specified decimal place or nearest degree.

Learn how to solve for unknown sides and angles in triangles using the Sine Rule and Cosine Rule. This guide provides a step-by-step solution to problems involving given angles and side lengths, ideal for Grades 9-10 students studying trigonometry.

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