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anonymous

  • 5 years ago

The length of the bridge is 48 ft and the height is 15 ft. It is made of 5 congruent triangles. Are these triangle acute, right, or obtuse? How many feet of material is needed to build one side of the bridge?

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  1. anonymous
    • 5 years ago
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    this is the diagram

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  2. anonymous
    • 5 years ago
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    please help me with this! it is really important

  3. anonymous
    • 5 years ago
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    The triangles are acute.

  4. anonymous
    • 5 years ago
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    sstarica might be showing why...

  5. anonymous
    • 5 years ago
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    lol, I was about to say that they are all the same that's all

  6. anonymous
    • 5 years ago
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    and was about to ask you why LOL

  7. anonymous
    • 5 years ago
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    oh :)

  8. anonymous
    • 5 years ago
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    ^_^ proceed.

  9. anonymous
    • 5 years ago
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    Okay QEvelyn, triangles are acute when each of their internal angles are less the 90 degrees. So the challenge here is to determine the angles. Here we go...

  10. anonymous
    • 5 years ago
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    You have three triangles on the bottom, and the sum of their bases equals 48. The base of each triangle is then, 48/3 = 16

  11. anonymous
    • 5 years ago
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    You're also told the height, which is 15. This is the same height you'd find from the base of the triangle to the apex. If you draw a perpendicular line from the apex (tip) to the bottom, it will bisect the base. You'll then have, in each triangle, two right-angled triangles with base = 8 height = 15 The hypotenuse is the side of the bigger triangle it came from. You need to find that. You can use Pythagoras' Theorem for that. So, \[s^2=8^2+15^2=289 \rightarrow s=17\]

  12. anonymous
    • 5 years ago
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    lol myininaya, you've answered in the wrong place

  13. anonymous
    • 5 years ago
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    oh nvm >_< her answer is gone

  14. anonymous
    • 5 years ago
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    Since two of these triangles make up your larger one, because of symmetry, you have an isosceles triangle (putting the two right-angled ones back together again). The base is 16 and the sides are 17 each. Because the triangle is isosceles, the two angles at the base will be equal. Call them \[\alpha\]Let's call the angle at the top\[\theta\]By the law of cosines, \[16^2=17^2+17^2-2 \times 17^2 \cos \theta \rightarrow \cos \theta = \frac{161}{289}\]which implies\[\theta \approx 56.145^o\]Since the sum of the angles of a plane triangle equals 180 degrees, and since the triangle is isosceles, you have\[180^o=2 \alpha +56.145^o \rightarrow \alpha \approx 61.928^o\]Your three angles in each of the bottom triangles is then\[56.145^o, 61.928^o,61.928^o\]All of these angles are less than 90 degrees, so the triangle is acute.

  15. anonymous
    • 5 years ago
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    Since you're given that the triangles are congruent, proving this for one proves for all.

  16. anonymous
    • 5 years ago
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    and he strikes again ~ :)

  17. anonymous
    • 5 years ago
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    lol

  18. anonymous
    • 5 years ago
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    QEvelyn, clear? :)

  19. anonymous
    • 5 years ago
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    I think the questioner has fled.

  20. anonymous
    • 5 years ago
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    was afraid of all the writing lol

  21. anonymous
    • 5 years ago
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    you've scared me, but when I read it, it was all clear :)

  22. anonymous
    • 5 years ago
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    scared you?

  23. anonymous
    • 5 years ago
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    the HUGE reply came out of nowhere in a BLINK ._. LOL

  24. anonymous
    • 5 years ago
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    Problem is, all this writing can be done away with if you could draw on this thing.

  25. anonymous
    • 5 years ago
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    Haha

  26. anonymous
    • 5 years ago
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    yeah , I know lol ^_^

  27. anonymous
    • 5 years ago
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    he's prolly checking your reply now :)

  28. anonymous
    • 5 years ago
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    Do you want to finish it - I want to go to bed?!

  29. anonymous
    • 5 years ago
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    but it's already done?!

  30. anonymous
    • 5 years ago
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    There's something about area.

  31. anonymous
    • 5 years ago
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    well add up all the areas then,right?

  32. anonymous
    • 5 years ago
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    A = 120x5 = 600 ft^2 done!

  33. anonymous
    • 5 years ago
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    he'll need that much for that, I guess

  34. anonymous
    • 5 years ago
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    How many feet of material or something...

  35. anonymous
    • 5 years ago
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    wait, it's not .

  36. anonymous
    • 5 years ago
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    Could be one of those frame bridges.

  37. anonymous
    • 5 years ago
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    I figured the answer till the area of each, but not the material

  38. anonymous
    • 5 years ago
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    I get 182 feet for one side.

  39. anonymous
    • 5 years ago
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    Just check, I'm fried.

  40. anonymous
    • 5 years ago
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    lol, alright scoot

  41. anonymous
    • 5 years ago
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    Bye! Happy mathing.

  42. anonymous
    • 5 years ago
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    lol bye, I'll try to solve it though ^_^

  43. anonymous
    • 5 years ago
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    I can't seem to figure out how he got 182 ft

  44. anonymous
    • 5 years ago
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    sstarica, you'll kick yourself: it's just summing up each of the lengths.

  45. anonymous
    • 5 years ago
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    HI GUYS thank you very much it went all over my head and sorry im so late to respond. the teacher will go over it in class next week and ill tell you all what she got. thank you again and i know who to come to again for math help! oh yeah and im a she :)

  46. anonymous
    • 5 years ago
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    And I just became a fan of both of you so Iokisan, you are now a Hero!!!

  47. anonymous
    • 5 years ago
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    Oh, so you're the one who clicked me over! Thank you!

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