a hiker walks 14.7 km at an angle 35 degrees south of east. Find the east and north components of this walk.
Check your duplicate post.
east - 12.04
north - 8.43
To find the east and north components of the hiker's walk, we can use trigonometry.
1. First, we find the east component by multiplying the total distance walked (14.7 km) by the cosine of the angle.
East Component = 14.7 km * cos(35 degrees)
2. Next, we find the north component by multiplying the total distance walked (14.7 km) by the sine of the angle.
North Component = 14.7 km * sin(35 degrees)
Using a calculator, we can calculate the values:
East Component ≈ 12.009 km (rounded to 3 decimal places)
North Component ≈ -8.073 km (rounded to 3 decimal places)
Note: The north component is negative because it is south of the east direction.
To find the east and north components of the hike, we can use trigonometry. Let's break it down step by step:
Step 1: Identify the given information:
- The distance walked is 14.7 km.
- The angle is 35 degrees south of east.
Step 2: Determine the direction:
The angle given is south of east. Since the angle is specified as "south," it means it is directed opposite to the north. Therefore, the direction can be measured as 180 degrees minus the given angle. So, the direction is 180° - 35° = 145° east of north.
Step 3: Calculate the east and north components:
We'll use trigonometry ratios (sine and cosine) to find the east and north components.
The east component (E) is calculated as E = distance × cosine(angle).
The north component (N) is calculated as N = distance × sine(angle).
Given:
Distance = 14.7 km
Angle = 145° (east of north)
Cosine(145°) ≈ -0.5736
Sine(145°) ≈ 0.8192
Calculations:
E = 14.7 km × -0.5736 ≈ -8.42632 km (rounded to 5 decimal places)
N = 14.7 km × 0.8192 ≈ 12.00864 km (rounded to 5 decimal places)
Answer:
The east component of the walk is approximately -8.42632 km, and the north component is approximately 12.00864 km.