Trigonometry for Physics help (cos, sin, tan)?

Question

okay, we are doing some problems for physics..and im kind of lost...I need help because I have never taken a trig class in my life and this physics book I have doesnt help that much..heres the question.

1. A man walks 5 mi east, then 6 mi North and then 3 mi further East. Make a scale diagram of the man's path on graph paper.

I did this and got 14 mi.

part b) Calculate the straight-line distance from where the man started to where the man ends up. (Is this the same, grater than or less than your answer to part a.

I got 10 mi as my answer which is less than.

Now heres my trouble.

c) At his final position the man turns and points toward his starting point. What direction is he pointing? (Be clear and exact)

Now of course he is pointing southwest, but he wants the degrees west of south. And I have no idea how to get this, someone told me to use tangent, but im completely lost how tangent can get this for me...can someone help me out?

Answer 1

Calculate tan^-1 (8/6) - This will give you the angle between due South and the direction he is facing.

Angle = 53.1 degrees west of south.

Imagine it like a triangle, the distance walked east is 5+3 = 8, the distance walked north is 6. The opposite side of the triangle from the angle you want (8) divided by the adjacent side of the triangle from the angle you want (6) then put through the tan ^ -1 function gives you the angle.

Answer 2

You could do this by creating and adding up the vectors.

1 vector has the magnitude of 5, at 0 degrees. (since it's east)
1 vector has a magnitude of 6, at 90 degrees (since it's north)
and 1 vector has a magnitude of 3, at 0 degrees (since it's east.)

Doing this, you find that, when drawn, you could make a triangle's bases, with one of a magnitude of 8 at 0 degrees, and one of a magnitude of 6 degrees. You could then use the pythagorean theorem to solve for the resultant, which is 10, which you got.

To find the direction, you use tangent, which is the opposite side of the theta divided by the adjacent side.

This makes:

Tangent (theta) = 8/6. To solve for theta, which is the direction, you multiply both sides by the inverse of tangent. You get an answer of 53.1 degrees.

Answer 3

The angle from the starting point to the man's current position isx = arctan(3/4) = 36.86989765 degrees

S0 th angle he is pointing at is 180 + 36.86989765 =
216.866989765 degrees

So the angle between where the man is pointing and due West 36.86989765 degrees and the angle between where the man is pointing and due South is 53.13010235 degrees.

Answer 4

the attitude you like is the single on the splendid of your diagram (Northernmost) of the splendid triangle. The facet adjacent to the attitude is 6, the hypotenuse is 10. The facet adjacent divided by skill of the hypotenuse is a cosine. you like the attitude whose cosine is 6/10 or .6 looking down a trig table, the attitude closest to .6 cos is approximately fifty 3 ranges (clockwise from south) or 233 ranges on a compass. To do it utilising a tangent, that's the facet opposite the attitude divided by skill of the facet adjacent (8/6 or a million.333), the table shows the attitude whose tangent is closest to a million.333 is likewise fifty 3 ranges. to apply the sine, that's the facet opposite the attitude divided by skill of the hypotenuse (8/10 or .8), the attitude with a sine of .8 is approximately fifty 3.