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Babynini

  • one year ago

Height of a mountain To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 35 degrees. Estimate the height of the mountain.

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  1. Babynini
    • one year ago
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    |dw:1434728278112:dw|

  2. Babynini
    • one year ago
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    @rvc free?

  3. Babynini
    • one year ago
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    @zepdrix :)

  4. Babynini
    • one year ago
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    @Michele_Laino

  5. Babynini
    • one year ago
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    (the drawing was not given to me, it is my representation of the question)

  6. Michele_Laino
    • one year ago
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    I think that the right drawing is: |dw:1434728792636:dw|

  7. Babynini
    • one year ago
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    hrrm, ok. I thought of that but didn't want to assume it was a right angle.

  8. Babynini
    • one year ago
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    |dw:1434728933190:dw|

  9. Babynini
    • one year ago
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    right?

  10. Michele_Laino
    • one year ago
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    yes! correct!

  11. Michele_Laino
    • one year ago
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    then: h= x * tan(32)

  12. Michele_Laino
    • one year ago
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    oops: h= x* tan(35)

  13. Babynini
    • one year ago
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    Hm? why that? that's the second triangle

  14. Babynini
    • one year ago
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    you mean after we solve for x in tan(32) = h/(1000+x) then we do h= x*tan(35) ??

  15. Michele_Laino
    • one year ago
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    yes! |dw:1434729130312:dw|

  16. Michele_Laino
    • one year ago
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    we have the subsequent step: \[\begin{gathered} \left( {x + 1000} \right)\tan 32 = h = x\tan 35 \hfill \\ \hfill \\ \left( {x + 1000} \right)\tan 32 = x\tan 35 \hfill \\ \end{gathered} \]

  17. Michele_Laino
    • one year ago
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    we have to solve the last equation for x

  18. Babynini
    • one year ago
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    er well 1,000tan(32) = 624.87

  19. Michele_Laino
    • one year ago
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    ok! correct!

  20. Michele_Laino
    • one year ago
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    \[x\tan 32 + 624.87 = x\tan 35\]

  21. Babynini
    • one year ago
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    So why does that equal xtan35?

  22. Babynini
    • one year ago
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    and not h

  23. Michele_Laino
    • one year ago
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    since you don't know the value of x

  24. Babynini
    • one year ago
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    hm k. Now what do we do? :)

  25. Michele_Laino
    • one year ago
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    we have to subtract x*tan(32) from both sides, so we get: \[\begin{gathered} 624.87 = x\tan 35 - x\tan 32 \hfill \\ \hfill \\ 624.87 = x\left( {\tan 35 - \tan 32} \right) \hfill \\ \end{gathered} \]

  26. Michele_Laino
    • one year ago
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    then dividing both sides by (tan35-tan32), we get: \[x = \frac{{624.87}}{{\tan 35 - \tan 32}} = ...\]

  27. Babynini
    • one year ago
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    8294.19 !

  28. Babynini
    • one year ago
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    ft

  29. Michele_Laino
    • one year ago
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    ok! Now substitute that value into this formula: \[h = 8294.2 \times \tan 35 = ...\]

  30. Michele_Laino
    • one year ago
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    since: \[h = x\tan 35\]

  31. Babynini
    • one year ago
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    I plug it into that second one?

  32. Babynini
    • one year ago
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    = 5807.7 ft

  33. Michele_Laino
    • one year ago
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    that's right!

  34. Babynini
    • one year ago
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    yayaya :)

  35. Michele_Laino
    • one year ago
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    :)

  36. Babynini
    • one year ago
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    So what we did: tan(32) = h/(1000+x) (1000+x)tan(32)=h xtan32+625.87 = xtan(35) subtract xtan(32) from both sides 625.87 = xtan(35)-xtan(32) 625.87 = x(tan(35)-tan(32)) divide the 625 by the tans to get x = 8294 plug that into h=xtan(25) to get our result 5808ft

  37. Michele_Laino
    • one year ago
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    that's right, nevertheless it is 624.87 not 625.87

  38. rvc
    • one year ago
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    Thank you so much @Michele_Laino :)

  39. Michele_Laino
    • one year ago
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    :) @rvc

  40. Babynini
    • one year ago
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    Oh, right. Sorry, that was a typo :P thanks!!

  41. Michele_Laino
    • one year ago
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    thanks!!

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