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?

- anonymous

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- anonymous

this is the diagram

##### 1 Attachment

- anonymous

please help me with this! it is really important

- anonymous

The triangles are acute.

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## More answers

- anonymous

sstarica might be showing why...

- anonymous

lol, I was about to say that they are all the same that's all

- anonymous

and was about to ask you why LOL

- anonymous

oh :)

- anonymous

^_^ proceed.

- 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

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

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

lol myininaya, you've answered in the wrong place

- anonymous

oh nvm >_< her answer is gone

- 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

Since you're given that the triangles are congruent, proving this for one proves for all.

- anonymous

and he strikes again ~ :)

- anonymous

lol

- anonymous

QEvelyn, clear? :)

- anonymous

I think the questioner has fled.

- anonymous

was afraid of all the writing lol

- anonymous

you've scared me, but when I read it, it was all clear :)

- anonymous

scared you?

- anonymous

the HUGE reply came out of nowhere in a BLINK ._. LOL

- anonymous

Problem is, all this writing can be done away with if you could draw on this thing.

- anonymous

Haha

- anonymous

yeah , I know lol ^_^

- anonymous

he's prolly checking your reply now :)

- anonymous

Do you want to finish it - I want to go to bed?!

- anonymous

but it's already done?!

- anonymous

There's something about area.

- anonymous

well add up all the areas then,right?

- anonymous

A = 120x5 = 600 ft^2 done!

- anonymous

he'll need that much for that, I guess

- anonymous

How many feet of material or something...

- anonymous

wait, it's not .

- anonymous

Could be one of those frame bridges.

- anonymous

I figured the answer till the area of each, but not the material

- anonymous

I get 182 feet for one side.

- anonymous

Just check, I'm fried.

- anonymous

lol, alright scoot

- anonymous

Bye! Happy mathing.

- anonymous

lol bye, I'll try to solve it though ^_^

- anonymous

I can't seem to figure out how he got 182 ft

- anonymous

sstarica, you'll kick yourself: it's just summing up each of the lengths.

- 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

And I just became a fan of both of you so Iokisan, you are now a Hero!!!

- anonymous

Oh, so you're the one who clicked me over! Thank you!

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