## Trig Word Prob: ship goes 62 units at 12 deg, then 111 units

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Blackhole252
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### Trig Word Prob: ship goes 62 units at 12 deg, then 111 units

A ship travels 62 units on a bearing of 12deg, and then travels on a bearing of 102deg for 111 units. Find the distance from the starting point to the end point. Round to the nearest unit.
The answer apparently seems to be 127 units, but I have no idea how to get that.
A nice diagram/drawing.
Detailed steps on how you get the answer.

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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If you just need a rough picture, draw a line for "north", and then to approximate lines. The triangle you form will serve as a placeholder for the values and variables. Otherwise:

Get a piece of paper, a pencil (and eraser), a protractor, and a ruler.

Draw a dot for the starting point.

Draw a vertical line for "north".

Using your protractor, measure a twelve-degree angle to the right of the vertical line.

Draw the line for this angle. Measure out sixty-two units (such as 6.2 centimeters, or 3.1 cm, etc).

Draw a dot at the end of the sixty-two units.

Draw a vertical line from this second dot, for "north".

Using your protractor, measure a 102° angle to the right of the vertical line.

Draw the line for this angle. Measure out 111 units (such as 11.1 centimeters, or just a hair over 5.5 cm, etc).

Draw a dot at the end of the 111 units.

Draw a line from this third dot back to the first dot.

Label the diagram with the appropriate angles and lengths. The Law of Sines should serve to solve this exercise.

Blackhole252
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Joined: Fri Nov 13, 2009 10:31 pm
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### Re: Trig Word Prob: ship goes 62 units at 12 deg, then 111 units

Is this what you mean? If this is the correct diagram, I still can't solve it.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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You have two parallel lines, with a transversal. (Extent both vertical lines to confirm this, if you're not sure.)

So there is a twelve-degree angle to the bottom left of the second vertical. This tells you the size of the angle between the upper portion of the second vertical and the transversal. Subtracting, you can find the size of the rest of the angle currently labelled "102 deg" in your diagram. Since a straight line has an "angle" measure of 180°, you can find the size of the rest of the angle at the peak of the triangle.

Once you have this value, you should be able to see where to go from there....