A plane flies in a direction of N70°E for 80km,then on a bearing of S10°W for 150km.how far and in what direction is the plane from it's starting point?
draw a diagram and use the law of cosines.
To find the distance and direction of the plane from its starting point, we can use the concept of vector addition.
First, let's break down the given directions into their respective components:
1. N70°E can be broken down into two components:
- Northward component: 80 * sin(70°)
- Eastward component: 80 * cos(70°)
2. S10°W can be broken down into two components:
- Southward component: 150 * sin(10°)
- Westward component: 150 * cos(10°)
Now let's calculate the individual components:
Northward component = 80 * sin(70°) ≈ 72.93 km
Eastward component = 80 * cos(70°) ≈ 29.49 km
Southward component = 150 * sin(10°) ≈ 25.98 km
Westward component = 150 * cos(10°) ≈ 143.85 km
To find the total distance, we can sum up the magnitudes of the North/South and East/West components:
Total distance = sqrt((Northward component - Southward component)^2 + (Eastward component - Westward component)^2)
Total distance = sqrt((72.93 - 25.98)^2 + (29.49 - 143.85)^2) ≈ 154.52 km
To find the direction, we can use the arctan function:
Direction = arctan((Eastward component - Westward component) / (Northward component - Southward component))
Direction = arctan((29.49 - 143.85) / (72.93 - 25.98)) ≈ -63.68°
Therefore, the plane is approximately 154.52 km away from its starting point in a direction of 63.68° SOUTH of WEST.