Add the following vectors together: 35 km at 25 degrees N of E

15 km at 10 degrees E of N

The resultant vector is 45.3 N 40.74° North of East

Explanation:

The given vectors can be presented as follows;

35 km at 25 degrees N of E = 35 × cos(25)·  + 35 × sin(25)·  

15 km at 10 degrees E of N = 15 × cos(90 - 10)·  + 15 × sin(90 - 10)·  

15 km at 10 degrees E of N = 15 × cos(80)·  + 15 × sin(80)·  

The sum of the vectors becomes;

∑d = 35 × cos(25)· + 15 × cos(80)· + 35 × sin(25)·  + 15 × sin(80)·  

∑d ≈ 34.33· + 29.56·

The magnitude of the resultant vector = √(34.33² + 29.56²) ≈ 45.3 N

The direction = tan⁻¹(29.56/34.33) ≈ 40.74° North of East

The resultant vector = 45.3 N 40.74° North of East

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