To Calculate:
The angle of plastic wastebasket.
Answer to Problem 18CLT
The angle is
Explanation of Solution
Given Information:
Calculation:
To get the angle between the adjacent sides, proceed as follows:
Get the coordinates of the vertices of endpoints of the adjacent sides.
Side | Vertex | Vertex | Vertex | Vertex |
Side | ||||
Side | ||||
Side | ||||
Side | ||||
Side |
Now to get the normal vectors of the sides of the figure:
Normal vector of side
To determine the normal vector of the side procced as follows:
Get the diagonal vectors from their position vectors of the endpoints using the standard result.
Standard result:
For the two position vectors:
The vector joining them is,
Diagonal vectors joining
Diagonal vectors joining
Now, to get cross product between the diagonal vectors using standard result.
Standard result:
For the vectors:
Therefore,
Hence, the normal vector of the side
Now to get the normal vector to the side
Diagonal vectors joining
Diagonal vectors joining
Now get the cross product of two diagonal vectors.
Hence, the normal vector to the side
Now, get the angle between the two vectors using the standard result.
Angle between two vectors
Hence the angle is
Hence the angle between the two sides is
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
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