If the distance between location A to B is straight east 10 km. then from B to C is Nw 18KM How far would you be from point C to A.
Would you not need to more information then this to calculate this answer?
Use the Pythagorean Theorem.
(AB)^2 + (AC) ^2 = (BC)^2
substitute for AB and BC.
then solve for AC
no, just use the cosine law
AC^2 = 10^2 + 18^2 - 2(10)(18)cos45° ---- assuming that Nw meant "northwest"
= 169.44...
AC = √169.44.. = appr 13.02 km
Rose,
Sorry, I got in a hurry.
To calculate the distance from point C to A, we can use the concept of vector addition.
Given that the distance between A and B is 10 km straight east, and from B to C is 18 km northwest, we need to resolve these distances into their respective components.
1. From A to B (east): Since it is straight east, there is no north or south component to consider. Therefore, the component in the east direction is 10 km.
2. From B to C (northwest): Here, we need to break down the distance into its north and west components. The northwest direction can be considered as a combination of north and west. We can use Pythagoras' theorem to find the components:
- The north component: Given that the hypotenuse (distance from B to C) is 18 km, and the angle between the northwest direction and the north direction is 45 degrees, we can calculate the north component using trigonometry: north component = 18 km * sin(45°) ≈ 12.73 km.
- The west component: Similarly, using trigonometry, the west component can be calculated as: west component = 18 km * cos(45°) ≈ 12.73 km.
Now, to find the distance from C to A, we need to subtract the respective components:
- The east component from A to B: 10 km
- The west component from B to C: 12.73 km
So, the total distance from C to A would be: 10 km - 12.73 km = -2.73 km.
Note: The negative sign indicates that the direction from C to A is opposite to the east direction (towards the west). Therefore, the calculated result suggests that the distance from C to A would be 2.73 km west of point C.