Question

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?

Answer 1

this is the diagram

Answer 2

please help me with this! it is really important

Answer 3

The triangles are acute.

Answer 4

sstarica might be showing why...

Answer 5

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

Answer 6

and was about to ask you why LOL

Answer 7

oh :)

Answer 8

^_^ proceed.

Answer 9

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...

Answer 10

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

Answer 11

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,

\[s^2=8^2+15^2=289 \rightarrow s=17\]

Answer 12

lol myininaya, you've answered in the wrong place

Answer 13

oh nvm >_< her answer is gone

Answer 14

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.

Answer 15

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

Answer 16

and he strikes again ~ :)

Answer 17

lol

Answer 18

QEvelyn, clear? :)

Answer 19

I think the questioner has fled.

Answer 20

was afraid of all the writing lol

Answer 21

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

Answer 22

scared you?

Answer 23

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

Answer 24

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

Answer 25

Haha

Answer 26

yeah , I know lol ^_^

Answer 27

he's prolly checking your reply now :)

Answer 28

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

Answer 29

but it's already done?!

Answer 30

There's something about area.

Answer 31

well add up all the areas then,right?

Answer 32

A = 120x5 = 600 ft^2 done!

Answer 33

he'll need that much for that, I guess

Answer 34

How many feet of material or something...

Answer 35

wait, it's not .

Answer 36

Could be one of those frame bridges.

Answer 37

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

Answer 38

I get 182 feet for one side.

Answer 39

Just check, I'm fried.

Answer 40

lol, alright scoot

Answer 41

Bye! Happy mathing.

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

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 :)

Answer 46

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

Answer 47

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