Ada travels from A on a bearing of 60˚ to station B on a distance of 15km.she then leaves to station C 10km away from B due east of station
No, Ada travels from A on a heading of 60˚ because B lies on a bearing of 60˚ from A.
Then she apparently gets lost . . .
To determine Ada's final location at station C, we need to find the coordinates of station C after she leaves station B.
Let's break down the given information:
1. Ada travels from station A on a bearing of 60˚ to station B, covering a distance of 15 km.
2. Ada then leaves station B to station C, which is 10 km away from B, due east of station B.
To solve this problem, we can use the concept of vectors. Let's assume that the starting point, station A, is the origin of our coordinate system.
1. Vector AB (A -> B): To find the coordinates of B, we need to convert the given bearing of 60˚ into Cartesian coordinates. We can use basic trigonometry for this.
Given the bearing of 60˚, we have:
- The x-coordinate change (horizontal) is 15 km * cos(60˚).
- The y-coordinate change (vertical) is 15 km * sin(60˚).
Therefore, the coordinates of B can be obtained as follows:
- x-coordinate of B = x-coordinate of A + x-coordinate change.
- y-coordinate of B = y-coordinate of A + y-coordinate change.
2. Vector BC (B -> C): Since C is 10 km due east of B, we only need to modify the x-coordinate of B. We can add 10 km to the x-coordinate of B to reach C.
Therefore, the coordinates of C can be obtained as follows:
- x-coordinate of C = x-coordinate of B + 10 km (due east).
- y-coordinate of C = y-coordinate of B.
By calculating the values based on the information provided, we can determine the coordinates of station C, which will give us Ada's final location.