A fence post is 52.0 m from where you are standing, in a direction 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 m?
To find the distance of the second fence post from you, we can use trigonometry and the given information.
First, let's assume that you are at the origin of a coordinate system, with the positive x-axis pointing east and the positive y-axis pointing north.
Now, let's break down the given information:
1. The fence post is 52.0 m away from you in a direction 37.0 degrees north of east. This means that the post is 52.0 m away from you along the vector formed by the angle between the positive x-axis and the line connecting you and the post.
2. The second fence post is due south from you. This means that the second post is directly along the negative y-axis.
To find the distance of the second post from you (let's call it d), we need to find the y-coordinate of the first fence post and subtract it from the y-coordinate of the second fence post.
To do this, we can use the information given about the first fence post's position:
Using trigonometry, we can find the y-coordinate by multiplying the distance (52.0 m) by the sin of the angle (37.0 degrees):
y-coordinate of the first post = 52.0 m * sin(37.0 degrees)
Now, since the second fence post is due south from you, its y-coordinate is simply -d.
So, the equation becomes:
52.0 m * sin(37.0 degrees) = -d
We can rearrange this equation to solve for d:
d = -52.0 m * sin(37.0 degrees)
Plugging in the numbers:
d = -52.0 m * sin(37.0 degrees)
d ≈ -31.6 m
Therefore, the distance of the second post from you is approximately 31.6 meters.