From post C, An airplane and a helicopter travel to different islands.The plane travels.415 km N 60degrees45minutes E to island A. and the helicopter travels to island B at S 19degrees5minutes E for 120 km. what is the distance between tthe two island
To find the distance between the two islands, island A and island B, we can use the concept of vector addition. We will break down the vectors of the airplane and helicopter into their components, and then add them together to get the resultant vector.
Let's start with the vectors:
1. Airplane vector: 415 km N 60°45'
This vector can be broken down into two components:
- North component: 415 km * sin(60°45')
- East component: 415 km * cos(60°45')
2. Helicopter vector: 120 km S 19°5'E
This vector is already given in its components, being 120 km in the south direction and 120 km in the east direction.
Now, let's calculate the components of the airplane vector:
North component:
= 415 km * sin(60°45')
= 415 km * sin(60.75°)
= 415 km * 0.875
= 362.125 km (approximately)
East component:
= 415 km * cos(60°45')
= 415 km * cos(60.75°)
= 415 km * 0.483
= 200.745 km (approximately)
Now, let's add the components of the airplane and helicopter vectors together:
North component: 362.125 km + (-120 km) = 242.125 km
East component: 200.745 km + 0 km = 200.745 km
To find the resultant distance between the two islands, we can use the Pythagorean theorem:
Resultant distance = √(North component^2 + East component^2)
= √(242.125 km^2 + 200.745 km^2)
= √(58596.810625 km^2)
= 242.159 km (approximately)
Therefore, the distance between the two islands, island A and island B, is approximately 242.159 kilometers.