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anonymous

  • 4 years ago

the rectangular box has a 2x2 base and height of 1. cosine of angle between AC and AB is...

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  1. anonymous
    • 4 years ago
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  2. anonymous
    • 4 years ago
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    hints please, trying to solve on my own...

  3. Mertsj
    • 4 years ago
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    We need to see the rest of the problem

  4. anonymous
    • 4 years ago
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    i posted attachment

  5. Mertsj
    • 4 years ago
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    I know and it's not on that either

  6. anonymous
    • 4 years ago
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    yes it is

  7. anonymous
    • 4 years ago
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    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(?)

  8. anonymous
    • 4 years ago
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    divide the problem into two right triangles

  9. anonymous
    • 4 years ago
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    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.

  10. anonymous
    • 4 years ago
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    whoops. project the line down onto the base rectangle of the prism! sorry

  11. anonymous
    • 4 years ago
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    or use dot product of AC with AB

  12. Mertsj
    • 4 years ago
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    The cosine of the angle is 2/3

  13. anonymous
    • 4 years ago
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    ok, the dot product gives me the cosine? anything else i need to do after? and why dot produvct?

  14. anonymous
    • 4 years ago
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    because it gives you the cos of the angle, which is what you are trying to solve for

  15. anonymous
    • 4 years ago
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    |dw:1327112719359:dw|the dot product of A and B is C

  16. anonymous
    • 4 years ago
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    so,\[A*B=|AC||AB|\cos \theta\]

  17. anonymous
    • 4 years ago
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    let me know if you need more help from here

  18. anonymous
    • 4 years ago
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    Sorry I should have wrote \[AC*AB=|AC||AB|\cos \theta\]

  19. anonymous
    • 4 years ago
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    thx, still trying to understand...first how do i get AC...it would be sqrt(1^2+?^2)

  20. anonymous
    • 4 years ago
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    no

  21. anonymous
    • 4 years ago
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    o, sqrt(1+8)=3

  22. anonymous
    • 4 years ago
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    so AC=3

  23. anonymous
    • 4 years ago
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    AC=<2,2,1> so |AC|=(2^2+2^2+1^2)^1/2

  24. anonymous
    • 4 years ago
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    ok...i saw that dot product formula quite a few times but i don't get it. <AB>dot<AC>=|AB||AC|...and multiplied by cos...

  25. anonymous
    • 4 years ago
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    yeah, exactly. |AB||AC|cosa, where a i the angle between vectors AB and AC

  26. anonymous
    • 4 years ago
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    do you remember how to calculate the dot product part?

  27. anonymous
    • 4 years ago
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    yes. mult component wise and then add

  28. anonymous
    • 4 years ago
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    yep :)

  29. anonymous
    • 4 years ago
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    ok so have that on the left side...and then solve for cosa

  30. anonymous
    • 4 years ago
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    exactly

  31. anonymous
    • 4 years ago
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    ok ok. so use sina if the question asks to find the sine of the angle?

  32. anonymous
    • 4 years ago
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    no..the dot product only gives you cosines

  33. anonymous
    • 4 years ago
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    so if i'm asked for sine...?

  34. anonymous
    • 4 years ago
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    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.

  35. anonymous
    • 4 years ago
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    ok, thx you closed the gap a lot for me just from this problem

  36. anonymous
    • 4 years ago
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    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

  37. anonymous
    • 4 years ago
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    np

  38. anonymous
    • 4 years ago
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    i get .84 but the closest out of the choices i have is 2/sqrt(5)...or none of the above

  39. anonymous
    • 4 years ago
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    I get cos a = 2/3

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