A fence post is 50.0 m from where you are standing, in s direction of 37.0 degree north of east. A second fence post is due south from you. What is the distance of the second post from you,if the distance between the two posts is 80.0?
draw the figure. You have two sides, and the included angle. Use the law of cosines to find the side opposite.
To find the distance of the second post from you, we can use the concept of vectors and trigonometry.
Let's start by visualizing the situation:
- You are standing at a point.
- The first fence post is located 50.0 m away from you, in a direction of 37.0 degrees north of east.
- The second fence post is due south from you.
- The distance between the two fence posts is 80.0 m.
To find the distance of the second post from you, we need to determine the horizontal and vertical components of the first fence post's position.
The horizontal component can be found using cosine:
cos(37.0 degrees) = adjacent / hypotenuse
adjacent = cos(37.0 degrees) * 50.0 m
The vertical component can be found using sine:
sin(37.0 degrees) = opposite / hypotenuse
opposite = sin(37.0 degrees) * 50.0 m
Now, we can subtract the horizontal component from the second fence post's position to get its distance from you. Since it is directly south, the vertical component will give us the distance:
distance of the second post from you = vertical component of the first post - distance between the two posts
distance of the second post from you = opposite - 80.0 m
Now, we can plug in the values:
distance of the second post from you = (sin(37.0 degrees) * 50.0 m) - 80.0 m
Calculating this expression will give us the final answer.