Answer:
The correct answer is option a. 40.6 m.
Step-by-step explanation:
To find the length of the western component of the vector, we need to use trigonometry. The given information states that the line is 45.0 meters long and is 25.5° south of west.
1. Let's draw a diagram to visualize the situation.
- Start with a horizontal line representing the west direction.
- From the starting point of the west line, draw a line downwards at a 25.5° angle. This line represents the vector the surveyor has drawn.
- Label the length of the vector as 45.0 meters.
2. Now, we need to find the length of the western component of the vector.
- The western component is the side adjacent to the given angle.
- We can use the cosine function to find the length of the western component: cosine(angle) = adjacent/hypotenuse.
- In this case, the adjacent side is the length of the western component, and the hypotenuse is the given length of the vector.
3. Apply the cosine function:
- cos(25.5°) = adjacent/45.0
- Rearrange the equation to solve for the adjacent side:
adjacent = cos(25.5°) × 45.0
4. Calculate the length of the western component:
- Use a calculator to find the cosine of 25.5° and multiply it by 45.0.
- The result is approximately 40.6.
Therefore, the length of the western component of the vector is approximately 40.6 meters.
The correct answer is option a. 40.6 m.
