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To solve this problem, let’s go through the steps to find both the magnitude of the resultant force and the angle it makes with the smaller force.

### Given:
- Two forces acting at right angles: \( F_1 = 36 \, \text{N} \) and \( F_2 = 45 \, \text{N} \).

### Steps:
1. **Calculate the Magnitude of the Resultant Force** \( R \):
   Since the forces are perpendicular, we can use the Pythagorean theorem:
   \[
   R = \sqrt{F_1^2 + F_2^2}
   \]
   Substituting the values:
   \[
   R = \sqrt{36^2 + 45^2}
   \]
   \[
   R = \sqrt{1296 + 2025}
   \]
   \[
   R = \sqrt{3321}
   \]
   \[
   R \approx 58 \, \text{N}
   \]
   So, the magnitude of the resultant force is approximately **58 N**.

2. **Calculate the Angle** \( \theta \) **the Resultant Makes with the Smaller Force**:
   We can use the tangent function since we know both forces:
   \[
   \tan(\theta) = \frac{F_2}{F_1}
   \]
   Substituting the values:
   \[
   \tan(\theta) = \frac{45}{36}
   \]
   \[
   \theta = \tan^{-1}\left(\frac{45}{36}\right)
   \]
   \[
   \theta \approx \tan^{-1}(1.25)
   \]
   \[
   \theta \approx 51^\circ
   \]
   So, the angle the resultant makes with the smaller force is approximately **51°**.

### Answers:
- The magnitude of the resultant force is **58 N**.
- The angle the resultant makes with the smaller force is **51°**.

Would you like more details on the calculations, or do you have any further questions?

Here are five related questions that expand on this topic:
1. What if the forces acted at a different angle, like 30°? How would that affect the resultant?
2. How would the solution change if there were three forces acting on the object?
3. What if one of the forces was negative, indicating it was acting in the opposite direction?
4. How can we calculate the components of the resultant force along the directions of the original forces?
5. How is this concept applied in real-world scenarios, like in engineering or physics problems?

**Tip:** In problems involving forces at right angles, the Pythagorean theorem and trigonometric functions are powerful tools for finding resultants and angles.

Two forces of 36 N (newtons) and 45 N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the smaller force.

Learn how to find the magnitude of the resultant force when two perpendicular forces of 36 N and 45 N act on an object. This step-by-step solution covers vector addition, the Pythagorean theorem, and trigonometric concepts. Suitable for high school students.

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