Another one for you :P, add these two vectors using trigonometry (again)... 9N[S2W] and 11N[N31W]...Again, I am confused about the angles, I am not sure what value I should use for the cosine and sine law. THANKS AGAIN!!
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]
To add these two vectors using trigonometry, we can break them down into their horizontal and vertical components.
Let's start with the vector 9N[S2W]. The direction indicates that it is pointing 2 degrees west of south. We can break it down into its horizontal and vertical components using trigonometry.
The horizontal component can be found using cosine. Since the angle is measured west of south, we need to use the angle's complement (90° - 2° = 88°) when applying the cosine function. The horizontal component is given by:
Horizontal component = 9N * cos(88°)
The vertical component can be found using sine. Using the same logic mentioned above, the vertical component is given by:
Vertical component = 9N * sin(88°)
Now, let's move on to the vector 11N[N31W]. This vector is pointing 31 degrees west of north.
Following the same steps as before, we can find its horizontal and vertical components using trigonometry:
Horizontal component = 11N * cos(31°)
Vertical component = 11N * sin(31°)
Now that we have obtained the horizontal and vertical components for both vectors, we can add them separately.
Sum of horizontal components = Horizontal component of 9N[S2W] + Horizontal component of 11N[N31W]
Sum of vertical components = Vertical component of 9N[S2W] + Vertical component of 11N[N31W]
The resultant vector will have its horizontal component equal to the sum of the horizontal components, and its vertical component equal to the sum of the vertical components. Finally, use trigonometry to find the magnitude and direction of the resultant vector.