Question

Hello there. I am working a physics problem and would like some help figuring out if I need to use the law of cosines or something else. Also I am blind and can't see equation grapics/ pictures. So for a tutor to help I need them to type out the equations to solve this question. So the question is: You are lost at night in a large, open field. Your GPS tell you that you are 122.0 m from your truck, in a direction 58.0∘ east of south. You walk 74.0 m due west along a ditch.Part AHow much farther must you walk to reach your truck? And what direction in degrees? Thanks. O also is there a way to do this with calculus?

Answer 1

We will have the following:

First, using the law of cosines we find the lenght of the missing side:

c = (a^2 + b^2 - 2a*b*cos(C))^(1/2)

That is:

c = (122^2 + 74^2 - 2(122)(77)cos(58))^(1/2)

c = 103.8834817

c is approximately 103.9 meters in legth.

Now, using the law of sines, we calculate the angle of inclination of this segment:

103.8834817 / sin(58) = 122.0 / sin(x)

so

sin(x) = 122.0 * sin(58) / 103.8834817

Then

x = Arcsin(122.0 * sin(58) / 103.8834817)

Finally we get that the measure