One of the rectangular components of a force of 40 N is 20 N. Find the angle it makes with the component.

Answer

To solve the problem, we need to find the angle θ that the resultant force makes with one of its rectangular components. Here’s a step-by-step solution:

### Step 1: Understand the Components
We have a resultant force (R) of 40 N and one of its rectangular components (H) which is given as 20 N. We will assume that the 20 N component is the horizontal component.

### Step 2: Use the Relationship Between Components
The relationship between the resultant force and its horizontal component can be expressed using the cosine of the angle θ:
\[ H = R \cdot \cos(\theta) \]
Where:
- \( H \) = horizontal component (20 N)
- \( R \) = resultant force (40 N)
- \( \theta \) = angle between the resultant and the horizontal component

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ 20 = 40 \cdot \cos(\theta) \]

### Step 4: Solve for Cosine
To isolate \( \cos(\theta) \), divide both sides by 40:
\[ \cos(\theta) = \frac{20}{40} \]
\[ \cos(\theta) = \frac{1}{2} \]

### Step 5: Find the Angle
Now, we need to find the angle \( \theta \) for which \( \cos(\theta) = \frac{1}{2} \). The angle that satisfies this condition is:
\[ \theta = 60^\circ \]

### Final Answer
Thus, the angle that the force makes with the horizontal component is:
\[ \theta = 60^\circ \]

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