a ship sails 22km from A on a bearing of 42°, and a further 30 km on a bearing of 90° to arrive at B. What is the distance and bearing of B from A ??
Plz give answer step by step and I'll be thankful to you. Also brainly creators you can answer.
Answers
Step-by-step explanation:
The first segment of 22km at 42 degrees can be decomposed into x and y (north and east) components. You could directly apply SohCahToa, but it’d be counterintuitive as your angle reference is based on 90 degrees (azimuth / north). To counteract this, transform your bearings to be based off of 0 degrees (East). Because North and East are complimentary (α + β = 90), you can do this by subtracting your bearing of 42 degrees (α) from 90 to give a new bearing of 48 degrees (β).
Now, The first thing to find is the y-component of the first segment. We know the hypotenuse (22) and the angle (β), and need the opposite leg of the triangle. SOH stands for Sin = Opposite over Hypotenuse. By multiplying both side by the hypotenuse, we find the y-component. The same can be done with the x-component and cosine.
The more problems you work in this fashion, the more comfortable you’ll become with the fact that as long as your angles are referenced to 0 degrees (East), the x component will always be the cosine component, and the y-component will always be from a sin function - especially if you take Newtonian physics at a collegiate level. Fun stuff.
Once we have the x and y components of the first segment, we can add in the purely x-component of the second segment to find our total Δx and Δy. To find the length of this summed hypotenuse, apply the pythagorean theorem (a2+b2=c2) This can be rearranged to solve for c (the hypotenuse) by taking the square root of both sides. plug and chug, and you get a total distance of 47.62 km. from point A to point B.