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To solve this problem, let's break down the forces given and their respective directions.

### Given Data:
1. \( F_1 = 15\sqrt{2} \, \text{N} \), directed at \( 45^\circ \) above the positive x-axis.
2. \( F_2 = 10 \, \text{N} \), directed along the negative x-axis.
3. \( F_3 = 20 \, \text{N} \), directed along the negative y-axis.

### Step-by-Step Solution:
We need to resolve each force into its x and y components and then sum these components to find the resultant force and its angle relative to the positive x-axis.

#### 1. Resolving \( F_1 \):
Since \( F_1 \) is at a \( 45^\circ \) angle to the positive x-axis:
\[
F_{1x} = 15\sqrt{2} \cos(45^\circ) = 15 \, \text{N}
\]
\[
F_{1y} = 15\sqrt{2} \sin(45^\circ) = 15 \, \text{N}
\]

#### 2. Resolving \( F_2 \):
Since \( F_2 \) is directed along the negative x-axis:
\[
F_{2x} = -10 \, \text{N}
\]
\[
F_{2y} = 0 \, \text{N}
\]

#### 3. Resolving \( F_3 \):
Since \( F_3 \) is directed along the negative y-axis:
\[
F_{3x} = 0 \, \text{N}
\]
\[
F_{3y} = -20 \, \text{N}
\]

### 4. Summing the Components:
Now, we sum the x and y components separately.

#### Resultant x-component (\( R_x \)):
\[
R_x = F_{1x} + F_{2x} + F_{3x} = 15 - 10 + 0 = 5 \, \text{N}
\]

#### Resultant y-component (\( R_y \)):
\[
R_y = F_{1y} + F_{2y} + F_{3y} = 15 + 0 - 20 = -5 \, \text{N}
\]

### 5. Calculating the Resultant Force \( R \):
The magnitude of the resultant force \( R \) is given by:
\[
R = \sqrt{R_x^2 + R_y^2} = \sqrt{5^2 + (-5)^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \, \text{N}
\]

### 6. Finding the Angle \( \theta \):
The angle \( \theta \) relative to the positive x-axis is calculated using:
\[
\theta = \tan^{-1} \left( \frac{R_y}{R_x} \right) = \tan^{-1} \left( \frac{-5}{5} \right) = \tan^{-1}(-1) = -45^\circ
\]

Since the angle is negative, the resultant force is directed \( 45^\circ \) below the positive x-axis.

### Final Answer:
- **Magnitude of the resultant force, \( R \):** \( 5\sqrt{2} \, \text{N} \)
- **Direction relative to the positive x-axis:** \( 45^\circ \) below the positive x-axis.

Would you like more details on any step or further clarification?

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Here are some related questions for further understanding:

1. How would the result change if \( F_2 \) were directed along the positive x-axis?
2. How can we find the direction if the resultant vector were in a different quadrant?
3. What is the physical interpretation of resolving forces into components?
4. How does the angle impact the effective force in the x and y directions?
5. Can you explain why the \( 45^\circ \) angle resulted in equal x and y components?

**Tip:** When breaking down forces, always use trigonometric identities for angles and be mindful of direction (positive or negative signs).

Jika F1 = 15√2 N; F2 = 10 N; F3 = 20 N, maka besar resultan dan arahnya terhadap sumbu x positif adalah …

Learn how to calculate the resultant force and its direction given three forces with specific magnitudes and directions. This problem demonstrates vector resolution and trigonometry, including how to find components and angles relative to the positive x-axis. Suitable for high school physics students.

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