anonymous
  • anonymous
the rectangular box has a 2x2 base and height of 1. cosine of angle between AC and AB is...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
hints please, trying to solve on my own...
Mertsj
  • Mertsj
We need to see the rest of the problem

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anonymous
  • anonymous
i posted attachment
Mertsj
  • Mertsj
I know and it's not on that either
anonymous
  • anonymous
yes it is
anonymous
  • anonymous
you sure? i'm pretty sure it's solveable, just can't remember how...i believe the angle between the vector and AB (i'll label x axis) would be roh(?)
anonymous
  • anonymous
divide the problem into two right triangles
anonymous
  • anonymous
elica85. First, project the line down onto the base square of the triangle. Find the hypotenuse of the triangle that is formed by doing this. This is our adjacent quantity. We know the opposite quantity. Now we can use the tangent function.
anonymous
  • anonymous
whoops. project the line down onto the base rectangle of the prism! sorry
anonymous
  • anonymous
or use dot product of AC with AB
Mertsj
  • Mertsj
The cosine of the angle is 2/3
anonymous
  • anonymous
ok, the dot product gives me the cosine? anything else i need to do after? and why dot produvct?
anonymous
  • anonymous
because it gives you the cos of the angle, which is what you are trying to solve for
anonymous
  • anonymous
|dw:1327112719359:dw|the dot product of A and B is C
anonymous
  • anonymous
so,\[A*B=|AC||AB|\cos \theta\]
anonymous
  • anonymous
let me know if you need more help from here
anonymous
  • anonymous
Sorry I should have wrote \[AC*AB=|AC||AB|\cos \theta\]
anonymous
  • anonymous
thx, still trying to understand...first how do i get AC...it would be sqrt(1^2+?^2)
anonymous
  • anonymous
no
anonymous
  • anonymous
o, sqrt(1+8)=3
anonymous
  • anonymous
so AC=3
anonymous
  • anonymous
AC=<2,2,1> so |AC|=(2^2+2^2+1^2)^1/2
anonymous
  • anonymous
ok...i saw that dot product formula quite a few times but i don't get it. dot=|AB||AC|...and multiplied by cos...
anonymous
  • anonymous
yeah, exactly. |AB||AC|cosa, where a i the angle between vectors AB and AC
anonymous
  • anonymous
do you remember how to calculate the dot product part?
anonymous
  • anonymous
yes. mult component wise and then add
anonymous
  • anonymous
yep :)
anonymous
  • anonymous
ok so have that on the left side...and then solve for cosa
anonymous
  • anonymous
exactly
anonymous
  • anonymous
ok ok. so use sina if the question asks to find the sine of the angle?
anonymous
  • anonymous
no..the dot product only gives you cosines
anonymous
  • anonymous
so if i'm asked for sine...?
anonymous
  • anonymous
then you need to use another relation. if you have corresponding angles for example, you can relate the cos of one angle to the sin of another.
anonymous
  • anonymous
ok, thx you closed the gap a lot for me just from this problem
anonymous
  • anonymous
or the question might involve the cross-product of two vectors which involve the sin of the angle between the two vectors..depends on the problem
anonymous
  • anonymous
np
anonymous
  • anonymous
i get .84 but the closest out of the choices i have is 2/sqrt(5)...or none of the above
anonymous
  • anonymous
I get cos a = 2/3

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