"Bearing" question - finding distance between two objects

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In summary, the motorboat is initially 10 km South of the lighthouse and is traveling on a course of 53 degrees clockwise from North. The question is asking for the shortest distance between the motorboat and the lighthouse. To solve this, we can use trigonometry to find the length of the leg opposite the angle of 53 degrees in a right triangle with a hypotenuse of 10 km.
  • #1
tantrik
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Dear friends,

I am having problem solving the following question related to "bearing" in trigonometry.

A motorboat is 10 km South of a lighthouse and is on a course of 053 degrees. What is the shortest distance between the motorboat and the lighthouse?

My confusion is how does a boat travel 10 km South of a lighthouse and making an angle of 53 degrees clockwise from North. Is there something wrong with the question itself?

Thanks in advance.
 
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  • #2
I think the $10 \, \text{km}$ distance is the initial position of the motorboat. It'll travel in a direction $53^{\circ}$ clockwise of North, passing by the lighthouse. There will be one point in its travel where it will be the closest to the lighthouse. How far away is the lighthouse at that point?
 
  • #3
Draw a line from the lighthouse "due south" to the present position of the ship. Draw the line showing the path of the ship. Finally, draw the line from the lighthouse perpendicular to the path of the ship. You now have a right triangle. The first line, "due south", is the hypotenuse and is 10km long. The two other lines are the legs of the right triangle. Since the path of the ship makes a 53 degree angle with north, the angle at the current position of the ship is 53 degrees.

So you have a right triangle with angle 53 degrees, the hypotenuse of length 10 and you want to find the length of the leg opposite that angle. Sounds like a sine!
 

FAQ: "Bearing" question - finding distance between two objects

What is bearing?

Bearing is a term used in navigation to describe the direction of one object in relation to another object. It is typically measured in degrees from north and can be used to find the distance between two objects.

What is the difference between true bearing and magnetic bearing?

True bearing is the direction of an object in relation to true north, while magnetic bearing is the direction of an object in relation to magnetic north. Magnetic north can vary from true north due to the Earth's magnetic field, so magnetic bearings may need to be adjusted to calculate a true bearing.

How do you determine the distance between two objects using bearing?

To determine the distance between two objects using bearing, you will need to know the bearing of each object from a common reference point, as well as the distance between the two objects at that reference point. Using trigonometric functions, you can then calculate the distance between the two objects.

What tools can be used to measure bearing?

There are several tools that can be used to measure bearing, including a compass, a sextant, and a theodolite. These tools use different methods, such as magnetic fields or celestial objects, to determine the bearing of an object.

Are there any limitations to using bearing to find distance between two objects?

Yes, there are limitations to using bearing to find distance between two objects. These include factors such as the curvature of the Earth, the accuracy of the measuring tools, and potential human error. In some cases, other methods such as GPS may be more accurate for determining distance between two objects.

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