Calculate Total Boat Trip Distance: 70° & 272° Directions

  • Thread starter FrostScYthe
  • Start date
In summary, a boat travels from a dock in a direction of 70°, then changes direction to 272° and ends up 150 km north of its starting position. Using the Sine Law, the total distance traveled can be calculated by measuring the angles clockwise from north and using the correct diagram. The original attempt at solving the problem may have been incorrect due to incorrect angle measurements.
  • #1
FrostScYthe
80
0

Homework Statement


A boat leaves the dock and sails in a direction of 70°. Once reaching its destination on the opposite shore, it sails
in a direction of 272° and docks 150 km north of its original starting position. What is the total distance the boat
has traveled?

Homework Equations


Sine Law


The Attempt at a Solution


I don't think I'm getting the right answer because I'm not representing the problem correctly. This is how I'm representing the problem then I just simply use AAS

http://img243.imageshack.us/my.php?image=untitledce7.jpg
 
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  • #2
Your angles are incorrect- they should be measured from north in a clockwise direction. Using this, you should be able to draw the correct diagram, where the final poistion is due north of the starting position.
 
  • #3
I assume the 272° is with respect to the 'horizontal axis'?
 

FAQ: Calculate Total Boat Trip Distance: 70° & 272° Directions

How do I calculate the total boat trip distance using 70° and 272° directions?

To calculate the total boat trip distance, you will need to use trigonometric functions such as sine, cosine, and tangent. First, draw a diagram of the boat trip with the given directions. Then, use the law of cosines to find the distance between the starting point and the end point. Finally, use the law of sines to find the distance between the two points along the curved path. Add these two distances together to get the total boat trip distance.

Can I use a calculator to calculate the total boat trip distance?

Yes, you can use a calculator to help with the calculations involved in finding the total boat trip distance. Make sure to use the appropriate trigonometric functions and double check your calculations to ensure accuracy.

Do I need to know the length of the boat to calculate the total boat trip distance?

No, you do not need to know the length of the boat to calculate the total boat trip distance. The distance is based on the directions given and the curved path traveled, not the length of the boat.

What units should I use for the total boat trip distance?

The units for the total boat trip distance will depend on the units used for the given directions. If the directions are given in degrees, then the distance will be in the same units, such as degrees. If the directions are given in radians, then the distance will be in radians as well.

Can I use this method for calculating boat trip distance for any direction?

Yes, this method can be used for calculating the boat trip distance for any direction. As long as you have the starting and ending directions, you can use the law of cosines and sines to find the total distance traveled along the curved path.

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