Sunday, November 21, 2010

A cosine and sine question with bearings?

Hey i'm finding this question difficult=



Debbie runs 8km on a bearing of 310 degrees.

She stops, changes direction and continues running for 10 km on a bearing of 55 degrees.

Find the distance and bearing on which Debbie should run to return to her starting point.



I know how to draw the triangle and how to use the cosine and sine rules, i just don't know how to interpret them into the question. Could someone explain i've been trying for hours :)A cosine and sine question with bearings?
These problems can be done by solving a triangle. You should have no problem finding the magnitude of the resultant. It is, however a vector problem, with all angles drawn from north. The initial side of the angle is on the y-axis and the angle is opened clockwise. With that in mind the component vectors are added attaching them tail to head. Debbie should run the reverse direction of the Resultant.

The problem can be done by adding these numbers in polar coordinates.

(8, 310) + (10, 55) = (8.5,115.5 )

Debbie needs to run: 8.5 km with bearing 295.5

I added the vectors in polar form with a graphing calculator as complex numbers in polar form r*e^(螛i). You can convert to rectangular form for adding, then convert your answer back to polar form.A cosine and sine question with bearings?
WRONG!

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