Add the following vectors , 7m/s [N30E] and 2m/s [S17E], using trigonometry. Once you draw these out into diagrams, you use the triangle law yes? How do you find the angles to use in the cosine and sine law? A little confused, thanks for the help.

I would break the two vectors into components N, and E. For instance, the N component of the first is 7cos30. Then, after finding the components, add the N, then the N. Then use trig to find the resultant.

Another way is to use the law of cosines and law of sines, but I don't recommend that.

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Vectors/VectorAdditionSteps.html

To add vectors using trigonometry, you can use the components of the vectors along the x and y directions. Let's break down the given vectors into their x and y components first:

1. For the vector 7m/s [N30E]:
- The north component is given by: N = 7 * sin(30°)
- The east component is given by: E = 7 * cos(30°)

2. For the vector 2m/s [S17E]:
- The south component is given by: S = 2 * sin(17°)
- The east component is given by: E = 2 * cos(17°)

Now, you can determine the resultant vector by adding the x and y components separately:

- The total north component is: N_total = N - S
- The total east component is: E_total = E + E

Using the obtained total north and east components, you can determine the magnitude and direction of the resultant vector, R, using the Pythagorean theorem and trigonometry:

1. Magnitude:
- R = sqrt(N_total^2 + E_total^2)

2. Direction:
- The angle (θ) between the resultant vector and the east direction can be found using:
- θ = atan(N_total / E_total)
- Ensure that you consider the proper quadrant for the angle depending on the signs of N_total and E_total.

Now that you have the magnitude and direction of the resultant vector, you can express it in the required format (e.g., [NθE]).

Regarding your question about using the triangle law, you can indeed use it to visualize the vectors by drawing them as line segments on a graph. This can help in understanding the given vectors and their resultant vector, making it easier to apply the trigonometric calculations mentioned above.

Remember to always verify your calculations and angle measurements to ensure accuracy.