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Course and Bearing Practice

Open the Course and Bearing Worksheet in a separate window so we can easily switch between the work and the words. Use this worksheet to experiment, to see how things move, to find patterns in the problems.

Also available is the Course and Bearing Practice construction, on which we can make up and check solutions to problems.  This is a practice worksheet, so we should calculate and draw on our own, before checking the worksheet numbers and diagrams.

The words on this page are color-coded to match the constructions on the linked worksheets, above.  These instructions are aligned to the first worksheet link.

Our Course and Bearing problems are worked in four steps.    

• finding the bearing to an object at initial sighting,
• calculating the distance traveled,
• finding the angle to the sighting after traveling,
• finding the distance to the object at second sighting.

Initial Bearing

• First, move the Course slider to our desired course (the angle from North, clockwise to the direction we are heading).
• Second, move the "Object Sighted" point to the desired distance from our boat.

• the North arrow always points North from our position, since we are holding the compass,
• bearing always points from our position to the Object Sighted,
• since we currently know how to solve only right triangles, the Object Sighted will be either directly to our left or  right, not at any other angles.  

• right angles (and 270º angles) and the
• Angle Addition Postulate (from Geometry).
• Essentially, we add 90º (object to the right) or 270º (object left).  Then, if we're outside the 0º-360º range, we add/subtract 360º to find a coterminal angle in our range.

Distance Traveled

• Multiply speed (miles per hour) time time (hours) to get distance traveled (miles).
• Make sure of the units!  If traveling at miles per hour for minutes,  we must convert the minutes into decimal hours.

Bearing after Traveling

• Move Our Boat to the desired distance traveled from the initial sighting.

• the North arrow STILL points North from our position, since we are holding the compass,
• our course angle has not changed,
• the new bearing angle is still measured from North at our position, clockwise to the Object Sighted.

• Notice the angles available to us:
• Course,
• Bearing,
• Theta (always acute),
• and the 180º from our course line clockwise to where we've just come from.
• In all cases, 
• we know all but Theta,
• we can add 2-3 of these angles to equal the sum of the other(s), 
• after setting up the Angle Addition equation, we can solve for Theta.

Distance to the Object Sighted

• our initial position, current position, and the Object Sighted form a right triangle,
• the right angle in that triangle is at our initial position,
• we know the distance we traveled between our two sightings (the adjacent leg of the right triangles)
• we also know the angle Theta, which is inside the right triangle at our position.

• Second Sighting distance is the hypotenuse -- use cos(Theta),
• Initial Sighting distance is the opposite side -- use tan(Theta).

Exploring Course-Bearing Problems

• we already know all of the angles at our position except for Theta,
• we can quickly solve for Theta using the Angle Addition Postulate,
• traveling forms a right triangles with our initial position (right angle), current position, and the Object Sighted,
• we can quickly solve for the opposite leg and hypotenuse using SOH-CAH-TOA.

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