Two forces of magnitudes 3N and 4N respectively are acting on a body. Calculate the resultant force if the angle between them is- `"90"`

Explanation

To calculate the resultant force when two forces of magnitudes 3N and 4N are acting at an angle of 90 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Magnitudes of the Forces:**
- Let \( F_1 = 3N \) (the first force)
- Let \( F_2 = 4N \) (the second force)

2. **Understand the Angle Between the Forces:**
- The angle \( \theta \) between the two forces is given as \( 90^\circ \).

3. **Use the Formula for Resultant Force:**
- The formula for the resultant \( R \) of two forces \( F_1 \) and \( F_2 \) acting at an angle \( \theta \) is given by:
\[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta} \]

4. **Substitute the Values into the Formula:**
- Since \( \theta = 90^\circ \), we know that \( \cos 90^\circ = 0 \).
- Therefore, the formula simplifies to:
\[ R = \sqrt{F_1^2 + F_2^2} \]

5. **Calculate \( F_1^2 \) and \( F_2^2 \):**
- Calculate \( F_1^2 = 3^2 = 9 \)
- Calculate \( F_2^2 = 4^2 = 16 \)

6. **Add the Squares of the Forces:**
- Now, add these values:
\[ F_1^2 + F_2^2 = 9 + 16 = 25 \]

7. **Take the Square Root:**
- Now, take the square root of the sum:
\[ R = \sqrt{25} = 5N \]

8. **Conclusion:**
- The resultant force when two forces of 3N and 4N act at an angle of 90 degrees is \( 5N \).