Question

Hello there. I am working a physics problem and would like some help figuring out if I am doing this question properly, 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 A How much farther must you walk to reach your truck? And what direction in degrees? What I have done so far is use the law of cosines to solve for 1 side and got 103.8834817. then I used the law of sins and asin to get 1.480671128 and that just doesn't seem right. Thanks.

Answer 1

We will have the following:

First, we will find the supplement of the angle given to determine the internal angle of the triangle that we can use, that is:

C = 180° - 58° => C = 122°

Now, we use the law of cosines to calculate the length of the missing side:

c = sqrt(a^2 + b^2 - 2a*b*cos(122°))

That is:

c = sqrt(74.0^2 + 122.0^2 - 2(74.0)(122.0)cos(122°))

so

c = 172.9977521 meters

so, the measurement of the missing side would be approximately 173 meters.

Now, using the law of sines we find the angle at which he should move towards the truck:

172.9977521 / sin(122°) = 122.0 / sin(x)

So:

sin(x) = 122.0*sin(122°) / 172.9977521

Then:

x = Arcsin(122.0*sin(122°) / 172.9977521)

So:

x = 36.73059875°

So, we finally would have that he must move approximately 173 meters towards the truck at an approximate angle of 36.7°.