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anonymous

  • one year ago

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced: Triangle ABC has length of BC equal to 16 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees and measure of angle DCB is 30 degrees. What is the length of the wood that is needed to replace AD?

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  1. anonymous
    • one year ago
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    @stacy.reed08

  2. anonymous
    • one year ago
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    6.8 inches 6.2 inches 3.2 inches 2.8 inches

  3. anonymous
    • one year ago
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    I thought maybe doing 15 divided by 2 would work but i got 7.5 inches and thats not an option so im assuming there's a step im missing

  4. anonymous
    • one year ago
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    I should have looked down at the picture...it took me forever to draw by hand.

  5. anonymous
    • one year ago
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    ok, so if you think about it, there is a little triangle inside the larger triangle ABC

  6. anonymous
    • one year ago
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    Yes i see that

  7. anonymous
    • one year ago
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    ok, let's draw that triangle out separately

  8. anonymous
    • one year ago
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    |dw:1440107397764:dw|

  9. anonymous
    • one year ago
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    I take that back...sorry, I thought we were trying to figure out line segment DC...just kidding, we want AD

  10. anonymous
    • one year ago
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    im guessing in order to find out the rotting piece needed to be replaced we have to find out how long side CD is?

  11. anonymous
    • one year ago
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    ok, I know the answer and there is probably an easier way to get there, but this is what makes sense in my mind...

  12. anonymous
    • one year ago
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    use the smaller triangle to figure out the length of DB.

  13. anonymous
    • one year ago
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    How do we do that

  14. anonymous
    • one year ago
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    OH

  15. anonymous
    • one year ago
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    |dw:1440107651617:dw|

  16. anonymous
    • one year ago
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    ok so BC is 16 inches DB is 30 inches and 180-16-30=134 so Dc is 134

  17. anonymous
    • one year ago
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    nope, we don't know DB...we know angle DCB is 30 degrees and we know side BC is 16 inches.

  18. anonymous
    • one year ago
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    but since the angle is 30 degress wouldn't the side across from it be 30 inches?

  19. anonymous
    • one year ago
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    |dw:1440107798750:dw|

  20. anonymous
    • one year ago
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    if we pull the little triangle out it's easier to work with

  21. anonymous
    • one year ago
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    and nope...the side across from it is going to be an ugly number that we'll round a little bit to make it easier to work with.

  22. anonymous
    • one year ago
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    ok lol

  23. anonymous
    • one year ago
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    so the missing side x and the angle are related how?

  24. anonymous
    • one year ago
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    because they're opposite from each other

  25. anonymous
    • one year ago
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    ok, and how are the angle and the 16 inch side related?

  26. anonymous
    • one year ago
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    they are adjacent to each other

  27. anonymous
    • one year ago
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    so you have opposite and adjacent which means what trig function?

  28. anonymous
    • one year ago
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    Toa= tangent

  29. anonymous
    • one year ago
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    ok so plug it in and actually solve it out to get a single number. It will be ugly looking so round to 2 digits past the decimal.

  30. anonymous
    • one year ago
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    How would i solve/calculate this?

  31. anonymous
    • one year ago
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    Actually one sec

  32. anonymous
    • one year ago
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    I've gotta grab something off the printer...I'll be back in a minute

  33. anonymous
    • one year ago
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    Alright

  34. anonymous
    • one year ago
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    30(tan)16=9?

  35. anonymous
    • one year ago
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    9.24 just to be a little more accurate

  36. anonymous
    • one year ago
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    sorry it took so long, I locked my keys in my room and had to go around.

  37. anonymous
    • one year ago
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    lol it's fine so what would be the answer here then?

  38. anonymous
    • one year ago
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    the largest option available is 6.8 inches.

  39. anonymous
    • one year ago
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    or highest rather

  40. anonymous
    • one year ago
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    ok, so right now you're only part way done...

  41. anonymous
    • one year ago
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    now let's look at the big triangle...

  42. anonymous
    • one year ago
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    Lol i just realized

  43. anonymous
    • one year ago
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    |dw:1440108392044:dw|

  44. anonymous
    • one year ago
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    so we have the adjacent and opposite again?

  45. anonymous
    • one year ago
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    yup.

  46. anonymous
    • one year ago
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    I have to be somewhere at 7 on the dot so in an hour i have to go, just letting you know

  47. anonymous
    • one year ago
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    And once again i deeply appreciate your patience in helping me solve my geometry problems

  48. anonymous
    • one year ago
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    So we would do 15(tan)30?

  49. anonymous
    • one year ago
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    I actually need to leave as soon as we're done with this problem. I'm in grad school and have a paper to write...plus it's past 5 and I'm still at school :(

  50. anonymous
    • one year ago
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    the angle isn't 30...we need all of angle C

  51. anonymous
    • one year ago
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    |dw:1440108572263:dw|

  52. anonymous
    • one year ago
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    ahh so 45, and sorry for taking up so much time lol

  53. anonymous
    • one year ago
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    you're fine. like I said before, I don't teach math anymore so this is actually fun for me. :) and yes, 45

  54. anonymous
    • one year ago
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    so what's the length of our missing side?

  55. anonymous
    • one year ago
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    45?

  56. anonymous
    • one year ago
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    nope...plug it in just like you did before...your set up was write, just the angle number was wrong. so 16 tan 45

  57. anonymous
    • one year ago
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    it comes out as 16

  58. anonymous
    • one year ago
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    yup. so know you know side AB (the entire side) is 16 inches and you know DB is 9.24 so that means AD is ?

  59. anonymous
    • one year ago
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    or when i put the calculator in Radian form, its 25.9 or 26

  60. anonymous
    • one year ago
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    oh ok disregard that comment then

  61. anonymous
    • one year ago
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    the angle was given in degrees so don't use radian form :)

  62. anonymous
    • one year ago
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    omg 6.76

  63. anonymous
    • one year ago
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    You are amazing holy christ

  64. anonymous
    • one year ago
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    i have 3 more answers but with my new found knowledge maybe i can solve them on my own lol

  65. anonymous
    • one year ago
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    questions not answers*

  66. anonymous
    • one year ago
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    well I wouldn't go that far...I realized just know that the big triangle ABC is a 45-45-90 triangle which means both legs are equal...

  67. anonymous
    • one year ago
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    we didn't need to do all that last part....

  68. anonymous
    • one year ago
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    lol its fine

  69. anonymous
    • one year ago
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    Do you mind staying for just 3 more questions?

  70. anonymous
    • one year ago
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    Like just answering them would be fine, as we're both on a time budget, but if you can't then i completely understand.

  71. anonymous
    • one year ago
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    Unfortunately, I really have to go. The custodian is starting to wonder why I'm still here :)

  72. anonymous
    • one year ago
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    lol alright see you then thanks for the help and time once again!

  73. anonymous
    • one year ago
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    no problem! Best of luck on the rest of your problems :)

  74. anonymous
    • one year ago
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    lol thank you

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