anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
this is the diagram
1 Attachment
anonymous
  • anonymous
please help me with this! it is really important
anonymous
  • anonymous
The triangles are acute.

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anonymous
  • anonymous
sstarica might be showing why...
anonymous
  • anonymous
lol, I was about to say that they are all the same that's all
anonymous
  • anonymous
and was about to ask you why LOL
anonymous
  • anonymous
oh :)
anonymous
  • anonymous
^_^ proceed.
anonymous
  • anonymous
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...
anonymous
  • anonymous
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
anonymous
  • anonymous
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, \[s^2=8^2+15^2=289 \rightarrow s=17\]
anonymous
  • anonymous
lol myininaya, you've answered in the wrong place
anonymous
  • anonymous
oh nvm >_< her answer is gone
anonymous
  • anonymous
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.
anonymous
  • anonymous
Since you're given that the triangles are congruent, proving this for one proves for all.
anonymous
  • anonymous
and he strikes again ~ :)
anonymous
  • anonymous
lol
anonymous
  • anonymous
QEvelyn, clear? :)
anonymous
  • anonymous
I think the questioner has fled.
anonymous
  • anonymous
was afraid of all the writing lol
anonymous
  • anonymous
you've scared me, but when I read it, it was all clear :)
anonymous
  • anonymous
scared you?
anonymous
  • anonymous
the HUGE reply came out of nowhere in a BLINK ._. LOL
anonymous
  • anonymous
Problem is, all this writing can be done away with if you could draw on this thing.
anonymous
  • anonymous
Haha
anonymous
  • anonymous
yeah , I know lol ^_^
anonymous
  • anonymous
he's prolly checking your reply now :)
anonymous
  • anonymous
Do you want to finish it - I want to go to bed?!
anonymous
  • anonymous
but it's already done?!
anonymous
  • anonymous
There's something about area.
anonymous
  • anonymous
well add up all the areas then,right?
anonymous
  • anonymous
A = 120x5 = 600 ft^2 done!
anonymous
  • anonymous
he'll need that much for that, I guess
anonymous
  • anonymous
How many feet of material or something...
anonymous
  • anonymous
wait, it's not .
anonymous
  • anonymous
Could be one of those frame bridges.
anonymous
  • anonymous
I figured the answer till the area of each, but not the material
anonymous
  • anonymous
I get 182 feet for one side.
anonymous
  • anonymous
Just check, I'm fried.
anonymous
  • anonymous
lol, alright scoot
anonymous
  • anonymous
Bye! Happy mathing.
anonymous
  • anonymous
lol bye, I'll try to solve it though ^_^
anonymous
  • anonymous
I can't seem to figure out how he got 182 ft
anonymous
  • anonymous
sstarica, you'll kick yourself: it's just summing up each of the lengths.
anonymous
  • anonymous
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 :)
anonymous
  • anonymous
And I just became a fan of both of you so Iokisan, you are now a Hero!!!
anonymous
  • anonymous
Oh, so you're the one who clicked me over! Thank you!

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