Please help me with the following mathematical question.

Question

Rescue Option 2: Rescue Boat

There is a rescue boat that is already out at sea at R. However, it receives distress calls from the yacht and another boat, at the same time.
The rescue boat must go to the nearest distress call first.
The boat is located at B, 350 km away, on a bearing of 120°T from R.
The yacht is located at Y on a bearing of 210°T and 170 km away from B.

 

 

 

a) Show that ∠RBY is a right-angle.
i. The North/South lines at R and B are parallel lines. Use your knowledge of co-interior angles to find: ∠PBR = ___°

ii. Using the number of degrees in a revolution, show ∠RBY = 90°

 

Thanks so much

Answer 1

The "bearing" means angle relative to North. Imagine a line linking R and B (from now on, I will call it RB). The angle between that RB and "north" is the bearing, which is 120 degrees. Now consider the information they give you: "The North/South lines at R and B are parallel lines." That means that the angle between RB and North as measured from the boat (i.e. point B) must supplement (i.e. add up to 180) the angle between RB and North as measured from the rescuer (i.e. point R).

 

Confusing? See if taking a look at this diagram helps! http://i.imgur.com/Z8bwYWr.png

 

From this, we can infer that the rescuer R has a bearing from the boat B of 60 degrees as measured counter-clockwise from North. If you measure clockwise, you would find the bearing is 300 degrees. I believe this is the answer they are looking for to part i.

 

Now, we also know that the yacht Y has a bearing of 210 degrees as measured from the boat B (the angle measured between North and the line I will now call BY). That means the yacht is 210 degrees measured clockwise from North. If you measured counter-clockwise, you would see that the yacht is 150 degrees away from North (360 - 210 = 150). This is why they say "Use the number of degrees in a revolution."

 

I've drawn another diagram to show this a little more clearly than I can explain: http://i.imgur.com/HR0VCWV.png

 

You now have one of two ways to calculate the angle between RB and BY. You may either measure clockwise, and subtract the bearing to BY from the bearing to RB (i.e. 300 - 210 = 90 degrees) or measure counter-clockwise, and subtract the bearing to RB from the bearing to BY (i.e. 150 - 60 = 90 degrees). Either way, you have shown that the angle RBY is a right angle.

 

I hope that helps!