SHOW WORK. THANKS One day you go hiking at a nearby nature preserve. At First, y

Question

SHOW WORK.  THANKS

One day you go hiking at a nearby nature preserve. At First, you follow the straight, clearly marked trails. From your starting point, you travel 2.00 miles down the 1st trail. Then you turn to your left by 30.0 degree to follow a 2nd trail for 1.20 miles. Next, you turn to your right by 160 degree and follow a 3rd trail for 2.10 miles. At this point you are getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead you deeper into the woods. You would like to take a shortcut directly through the woods (ignoring the trails). How far to your right should you turn, and how far do you have to walk, to go directly back to your starting point? Feel free to use the provided vector drawing board to help visualize your work. Turn to the right, then walk

Explanation / Answer

coordinate of 1st point = ( 0, 0)

coodinate of 2nd point = (0, 2)

coordinate of 3rd point

as 30 degree angle with y axis , thus coordinate cn by caluclate by cos and sin

= (=0.6, 1.032)

coordinate of 4th point

160 degree angle = 10 degree angle with y axis

thus

4th point = (-0.5908, 0.1792)

distance between 1st and 4th point = sqrt(x^2+y^2)

= sqrt(1.009008)

= 1 mile

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