SOLUTION: How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the sun’s rays are parallel to the vector [5, 3, −2]?

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Question 1163487: How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the sun’s rays are parallel to the vector [5, 3, −2]?
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall,
given that the sun’s rays are parallel to the vector [5, 3, −2]?
~~~~~~~~~~~~~ 

First, the projection of the given 3D-vector to the (x,y)-plane is the vector V = [5,3].

It defines the direction to the sun in this plane, and its length is  | V | =  =  = .



Next, if the angle of sun rays with the Earth surface (which we interpret as the plane (x,y)) is ,  then

     = .


From the other side, if L is the shadow length, then

     = ,



which implies for the shadow length

     L =  =  =  = 23.32 meters (rounded).    ANSWER

Solved.



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