To calculate the work done by Carlos, we can use the formula for work done when a force is applied at an angle:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the distance moved,
- \( \theta \) is the angle between the force and the direction of motion.
In this case:
- \( F = 2000 , \text{N} \)
- \( d = 30 , \text{m} \)
- \( \theta = 15^\circ \)
Now we need to calculate \( \cos(15^\circ) \):
\[ \cos(15^\circ) \approx 0.9659 \]
Now we can substitute the values into the work formula:
\[ W = 2000 , \text{N} \cdot 30 , \text{m} \cdot \cos(15^\circ) \] \[ W \approx 2000 \cdot 30 \cdot 0.9659 \] \[ W \approx 60000 \cdot 0.9659 \] \[ W \approx 57954 , \text{J} \]
Rounding to two significant figures gives us:
\[ W \approx 5.8 \times 10^4 , \text{J} \]
So, the amount of work Carlos did is \( \boxed{5.8 \times 10^4 , \text{J}} \).