Trigonometry : Practical Applications
Study concepts, example questions & explanations for Trigonometry
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Example Questions
Example Question #1 : Bearing
Three ships are positioned in the following way: Ship A is 240 miles due west of Ship C, and Ship B is due south of Ship C. Ship B bears 
Distance from Ship A to Ship B: 640.67 miles
Distance from Ship B to Ship C: 594.02 miles
Bearing from Ship B to Ship A:
Distance from Ship A to Ship B: 594.02 miles
Distance from Ship B to Ship C: 640.67 miles
Bearing from Ship B to Ship A:
Distance from Ship A to Ship B: 640.67 miles
Distance from Ship B to Ship C: 594.02 miles
Bearing from Ship B to Ship A:
Distance from Ship A to Ship B: 594.02 miles
Distance from Ship B to Ship C: 640.67 miles
Bearing from Ship B to Ship A:
Distance from Ship A to Ship B: 640.67 miles
Distance from Ship B to Ship C: 594.02 miles
Bearing from Ship B to Ship A:
To solve this problem, begin with a diagram, and label all known information. We know that we can label two angles as 
Next, we need to use trigonometry to find the answers to each question we're being asked. To find the distance AB, set up
Next, we can find the distance BC. There are two ways to do this since we know two angles of the triangle, but either way you need to use the tangent function.
Finally, we are asked to find the bearing from Ship B to A. Be careful, because in the initial problem we are given the Bearing from Ship A to Ship B. While the angle will remain the same, the direction is different because we are starting at a different initial point (B instead of A). With B as your starting point, A is north and west. Therefore the bearing from Ship B to Ship A is 
Therefore the correct distance between Ships A and B is 640.67 miles, the distance between ships B and C is 594.02 miles, and the bearing from Ship B to Ship A is 
Example Question #22 : Practical Applications
Three cruise ships are situated as follows: Sea Terraformer is 200 miles due north of Wave Catcher, and Island Pioneer is 345 miles due east of Wave Catcher. What is the bearing from Island Pioneer to Sea Terraformer, and what is the bearing from Sea Terraformer to Island Pioneer?
Bearing from Island Pioneer to Sea Terraformer:
Bearing from Sea Terraformer to Island Pioneer:
Bearing from Island Pioneer to Sea Terraformer:
Bearing from Sea Terraformer to Island Pioneer:
Bearing from Island Pioneer to Sea Terraformer:
Bearing from Sea Terraformer to Island Pioneer:
Bearing from Island Pioneer to Sea Terraformer:
Bearing from Sea Terraformer to Island Pioneer:
Bearing from Island Pioneer to Sea Terraformer:
Bearing from Sea Terraformer to Island Pioneer:
Begin by diagramming the given information; you'll see that the three ships create a right triangle. To solve the question, we need to find the unknown angles of the triangle, then frame our answers as the proper bearings.
First let's solve for the topmost angle in the diagram, which we'll call 
By alternate interior angles, the other diagrammed angle will also be equal to 
Now, put your cursor on Island Pioneer, and see if you need to move north or south, and then east or west to get to Sea Terraformer. You need to move north, then west. Therefore the bearing between Island Pioneer and Sea Terraformer is 
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