To add vectors using trigonometry, we need to break down each vector into its horizontal and vertical components. Let's start with the first vector, 9N[S2W].
For the angle, S2W means South 2 degrees West. To use trigonometry, we need to convert this angle into standard format (measured in degrees from the positive x-axis).
In standard format, South is 180 degrees and West is 270 degrees. Therefore, South 2 degrees West is 180 + 2 = 182 degrees.
Now, let's calculate the horizontal and vertical components of the first vector:
Horizontal component:
Magnitude * cosine(angle)
= 9N * cos(182°)
≈ -8.97N
Vertical component:
Magnitude * sine(angle)
= 9N * sin(182°)
≈ -0.29N
Now, let's move on to the second vector, 11N[N31W].
For the angle, N31W means North 31 degrees West.
In standard format, North is 0 degrees and West is 270 degrees. Therefore, North 31 degrees West is 0 - 31 = -31 degrees.
Now, let's calculate the horizontal and vertical components of the second vector:
Horizontal component:
Magnitude * cosine(angle)
= 11N * cos(-31°)
≈ 9.45N
Vertical component:
Magnitude * sine(angle)
= 11N * sin(-31°)
≈ -5.82N
To add the two vectors together, we simply add their horizontal components and vertical components separately:
Horizontal component: -8.97N + 9.45N = 0.48N
Vertical component: -0.29N - 5.82N = -6.11N
Therefore, the resultant vector is approximately 0.48N[S5.92W]