Vertical component of these resultant vectors: 
vector a = 60N, 245 degrees from +x-axis
vector b = 70N, 75 degrees North of east
vector c = 95N, 87 degrees West of North

To find the vertical component of each vector, we use the fact that the vertical component \( F_y \) of a vector \( F \) at an angle \( \theta \) from the horizontal axis can be computed using:

\[
F_y = F \cdot \sin(\theta)
\]

Let's go through each vector:

### Vector \( a \):
- Magnitude = \( 60 \, \text{N} \)
- Angle = \( 245^\circ \) from the \( +x \)-axis (counterclockwise)
  
Since \( 245^\circ \) is in the third quadrant, \( \sin(245^\circ) \) will be negative. We compute the vertical component as:
\[
F_{a_y} = 60 \cdot \sin(245^\circ)
\]

### Vector \( b \):
- Magnitude = \( 70 \, \text{N} \)
- Angle = \( 75^\circ \) North of East (from the positive x-axis)

This is equivalent to an angle of \( 75^\circ \) counterclockwise from the \( +x \)-axis. Therefore, we compute:
\[
F_{b_y} = 70 \cdot \sin(75^\circ)
\]

### Vector \( c \):
- Magnitude = \( 95 \, \text{N} \)
- Angle = \( 87^\circ \) West of North

This is equivalent to \( 90^\circ - 87^\circ = 3^\circ \) West of North (or \( 90^\circ + 3^\circ = 93^\circ \) from the positive x-axis). We compute:
\[
F_{c_y} = 95 \cdot \sin(93^\circ)
\]

Now, let's calculate each vertical component.The vertical components of the given vectors are as follows:

1. **Vector \( a \) (60N, 245° from +x-axis):**
   \[
   F_{a_y} = -54.38 \, \text{N}
   \]
   (negative because it's in the third quadrant)

2. **Vector \( b \) (70N, 75° North of East):**
   \[
   F_{b_y} = 67.61 \, \text{N}
   \]
   (positive, as it points upwards)

3. **Vector \( c \) (95N, 87° West of North):**
   \[
   F_{c_y} = 94.87 \, \text{N}
   \]
   (positive, as it is nearly vertical)

Would you like more details or have any further questions?

Here are five related questions to explore:
1. What is the horizontal component of each vector?
2. How do we calculate the resultant of all three vectors?
3. What does the sign of a vertical component indicate about the direction?
4. How can you convert angles from different reference points into standard form?
5. How do the magnitudes of the vectors affect the overall resultant vector?

**Tip**: When dealing with angles measured counterclockwise from the positive x-axis, always consider the quadrant to determine the sign of the sine or cosine components.

Vertical component of these resultant vectors: vector a = 60N, 245 degrees from +x-axis; vector b = 70N, 75 degrees North of east; vector c = 95N, 87 degrees West of North

Learn how to calculate the vertical components of vectors given their magnitudes and angles using trigonometric functions. This problem breaks down three vectors: 60N at 245 degrees, 70N at 75 degrees North of East, and 95N at 87 degrees West of North. Suitable for students in Grades 10-12.

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