the pilot of a private plane flies 20km in a direction 60 degrees north of east,then 30km straight east,then 10km straight north.how far and in what direction is the plane from the starting point

I didn't get the whole process

To find the total distance and direction of the plane from the starting point, we can break down each leg of the journey into its north and east components and then combine them.

1. Leg 1: The pilot flies 20km in a direction 60 degrees north of east.
- North component: 20km * sin(60 degrees) = 20km * 0.866 = 17.32km north
- East component: 20km * cos(60 degrees) = 20km * 0.5 = 10km east

2. Leg 2: The pilot flies 30km straight east.
- North component: 0km north
- East component: 30km east

3. Leg 3: The pilot flies 10km straight north.
- North component: 10km north
- East component: 0km east

Now, let's add up the north and east components:

Total North component = 17.32km + 10km = 27.32km north
Total East component = 10km + 30km = 40km east

To find the total distance, we can use the Pythagorean theorem:

Total distance = square root of ((Total North component)^2 + (Total East component)^2)
Total distance = square root of ((27.32km)^2 + (40km)^2)
Total distance = square root of (747.02km^2 + 1600km^2)
Total distance = square root of (2347.02km^2)
Total distance ≈ 48.45km

To find the direction, we can use trigonometry:

Direction = arctan(Total North component / Total East component)
Direction = arctan(27.32km / 40km)
Direction ≈ 34.23 degrees north of east

Therefore, the plane is approximately 48.45km away from the starting point in a direction that is approximately 34.23 degrees north of east.

To find the distance and direction of the plane from the starting point, we can break down the given information into components.

1. First, let's calculate the displacement in the North direction.
The plane flies 10 km straight north, so the northward component is 10 km.

2. Next, let's calculate the displacement in the East direction.
The plane flies 20 km in a direction 60 degrees north of east, which can be broken down into two components: the eastward and northward components.
The northward component can be found using trigonometry: 20 km * cos(60°) = 20 km * 0.5 = 10 km.
The eastward component can also be found using trigonometry: 20 km * sin(60°) = 20 km * 0.866 = 17.32 km.

3. Lastly, let's calculate the displacement in the East direction.
The plane flies 30 km straight east, so the eastward component is 30 km.

Now, let's add up the eastward and northward components to find the total displacement of the plane from the starting point.

North component: 10 km
East component: 17.32 km + 30 km = 47.32 km

To find the total distance, we can use the Pythagorean theorem:
Distance = sqrt((North component)^2 + (East component)^2)
Distance = sqrt((10 km)^2 + (47.32 km)^2)
Distance = sqrt(100 km^2 + 2238.9424 km^2)
Distance = sqrt(2338.9424 km^2)
Distance ≈ 48.36 km

To find the direction, we can use trigonometry:
Direction = atan(North component / East component)
Direction = atan(10 km / 47.32 km)
Direction ≈ 12.12 degrees north of east

Therefore, the plane is approximately 48.36 km away from the starting point, in a direction approximately 12.12 degrees north of east.

Disp. = 20km[60o] + 30km[0o] + 10km[90o].

Disp. = (20*Cos60+30) + (20*sin60+10)i.
Disp. = 40 + 27.3i = 48.5km[34.3o] N. of E.