Question: Using trigonometry, add these two vectors. 7m/s [N30E] and 2m/s [S17E]. THIS is my answer: 6m/s [N45E] is this the correct answer?

Well, close enough. I got 45.5 degrees and 5.82 m/s

By the way, I used vector components rather than laws of cosines as math people might do it. My thing is physics.

To add two vectors using trigonometry, we can break them down into their horizontal and vertical components and then add those components separately.

For the vector 7m/s [N30E]:
- The horizontal component can be found using cosine: 7 * cos(30°) = 7 * 0.866 = 6.062 m/s to the east.
- The vertical component can be found using sine: 7 * sin(30°) = 7 * 0.5 = 3.5 m/s to the north.

For the vector 2m/s [S17E]:
- The horizontal component can be found using cosine: 2 * cos(17°) = 2 * 0.955 = 1.91 m/s to the east.
- The vertical component can be found using sine: 2 * sin(17°) = 2 * 0.292 = 0.584 m/s to the south.

To add the horizontal components: 6.062 m/s + 1.91 m/s = 7.972 m/s to the east (rounded to three decimal places).
To add the vertical components: 3.5 m/s + (-0.584 m/s) = 2.916 m/s to the north.

Using these components, we can find the resultant magnitude and direction:
- The magnitude of the resultant vector is found using the Pythagorean theorem: sqrt((7.972)^2 + (2.916)^2) = 8.624 m/s (rounded to three decimal places).
- The direction of the resultant vector can be found using the inverse tangent: atan(2.916/7.972) = 18.366°.

Therefore, the correct answer is approximately 8.624 m/s [N18.4E].

To add two vectors using trigonometry, we need to break down each vector into its horizontal and vertical components. Then we can add the horizontal components separately and the vertical components separately to find the resultant vector.

Let's break down the given vectors:

Vector 1: 7m/s [N30E]
- The magnitude of the vector is 7m/s.
- The direction is N30E, which means it is 30 degrees east from the north direction.
- To find the horizontal and vertical components, we can use trigonometric ratios.
- The horizontal component (x-axis) can be found using cosine: 7m/s * cos(30°) = 6.06 m/s.
- The vertical component (y-axis) can be found using sine: 7m/s * sin(30°) = 3.5 m/s.

Vector 2: 2m/s [S17E]
- The magnitude of the vector is 2m/s.
- The direction is S17E, which means it is 17 degrees east from the south direction.
- Similarly, we can break down this vector.
- Horizontal component: 2m/s * cos(17°) = 1.91 m/s.
- Vertical component: 2m/s * sin(17°) = -0.5 m/s. (Negative because it's in the opposite direction of the positive y-axis.)

Now let's add the horizontal and vertical components separately:

Horizontal components:
6.06 m/s + 1.91 m/s = 7.97 m/s.

Vertical components:
3.5 m/s + (-0.5 m/s) = 3 m/s.

Now that we have the horizontal and vertical components of the resultant vector, we can calculate the magnitude and direction using trigonometry:

Magnitude: √(7.97^2 + 3^2) ≈ 8.72 m/s.
Direction: tan^(-1)(3/7.97) ≈ 21.75° east from the north direction.

The correct answer is approximately 8.72 m/s [N21.75E].

So, "6m/s [N45E]" is not the correct answer.