A boat leaves the harbor and travels 100 miles on a bearing of N 54 (degrees) E. How many miles north and many many miles east from harbor has the boat traveled

Given:
- d = 100 miles,
- \theta = 54^\circ.

We can calculate d_{north} and d_{east} using trigonometric functions:
- d_{north} = d \cdot \cos(\theta),
- d_{east} = d \cdot \sin(\theta).

Substitute the values:
- d_{north} = 100 \cdot \cos(54^\circ),
- d_{east} = 100 \cdot \sin(54^\circ).

Calculating:
- d_{north} \approx 100 \cdot 0.5878 \approx 58.78 miles,
- d_{east} \approx 100 \cdot 0.8090 \approx 80.90 miles.

Therefore, the boat has traveled approximately \boxed{58.78} miles north and \boxed{80.90} miles east.

\boxed{Answer}