Final answer:
To find how far north and east point B is from O, we can use the concepts of sine and cosine. By breaking down the vectors from O to B into their north and east components, we can use trigonometry to find the distance and bearing of B from O.
Step-by-step explanation:
To solve this problem, we can use trigonometry and vector addition. Let's break down the problem step by step:
a) To find how far north of O point B is, we can use the concept of sine. The distance north is given by the formula: north distance = total distance * sin(θ), where θ is the angle from the north direction. In this case, the angle is 025°. So, north distance = 400 km * sin(25°) = 168.28 km.
b) To find how far east of O point B is, we can use the concept of cosine. The distance east is given by the formula: east distance = total distance * cos(θ), where θ is the angle from the north direction. In this case, the angle is 025°. So, east distance = 400 km * cos(25°) = 358.34 km.
c) To find the distance and bearing of B from O, we can use vector addition. We can break down the vectors from O to B into their north and east components and then add them up to find the resultant vector. The distance is the magnitude of the resultant vector, and the bearing is the angle it makes with the north direction. The north component can be found using the formula: north component = total distance * sin(θ), and the east component can be found using the formula: east component = total distance * cos(θ). By adding the north and east components, we can find the resultant vector. Using the Pythagorean theorem, the magnitude of the resultant vector is found to be approximately 759.73 km. To find the bearing, we can use the concept of inverse tangent (arctan). The bearing is given by the formula: bearing = arctan(east component / north component). In this case, the bearing is approximately 8.05°.