The image shows a portion of a bridge supported by vertical pillars from the slope below. What is the length of the bridge between pillar B and pillar C?

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The image shows a portion of a bridge supported by vertical pillars from the slope below. What is the length of the bridge between pillar B and pillar C?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Use pythagoras theorem for this question, both of em are similar triangles
I honestly do not know how to.

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i cant really help you the image is really fuzzy
and i dont run csi enhancer
do you know how to do the process you were talking about ? could you explain to me how to ?
ok lets start by finding this angle|dw:1438434416019:dw|
29 feet 48 feet 56 feet 60 feet those are my options btw. And alright.
\[\cos^{-1} (\frac{ 40 }{ 50 }) is the \angle\]
cos^1 (40/50) is the angle
im really confused.
|dw:1438434482105:dw|
okay from a to b on the top is 40 feet, bottom is 50 feet. and b to c on bottom is 70 feet, does that help ?
\[\frac{ 50 }{ 120 } = \frac{ 40 }{ 40+x }\]
now you can solve for x
you can do that i hope
i got 80 .. i feel like im wrong ... I havent had a math class since my freshman year in high school, and this is my senior year, and i just honestly dont have any idea what im doing ... i feel really stupid right now.
lemme try solving\[\frac{ 50 }{ 120 } = \frac{ 40 }{ 40+x }\]\[50 = \frac{ 4800 }{ 40+x }\]\[50(40+x)=4800\]\[2000+50x=4800\]\[50x=2800\]\[x=56\]
thank you ... But can i ask how you did that process ? if its too much to explain thats fine.
alright you just cross multiple the denominator to each sides to cancel them out (the 1st 2 lines).
cause fractions are messy. then you move the constant to one side of the equation (3rd line), by minus-ing the constant (2000) from both sides.
thats how we end up with 50x=2800
This whole thing confuses me. I literally feel dumb. I don't understand any of this.
which part you do not understand?
All of it... I don't even have a teacher, like i have to teach myself all of this stuff. Im probably wasting your time honestly, I cant comprehend this kind of stuff.
ok ill write it in simpler form
You don't have to do that..
you gotta know how we come out with that first....
otherwise you will keep getting stuck
I just dont want to waste your time. And i don't think ill ever understand this.
well just take it easy, 1 thing at a time
okay..
ill explain to you how the\[\frac{ 50 }{ 120 } = \frac{ 40 }{ 40+x }\] is made first
the triangle in the diagram is a similar triangle, therefore they are proportional to each other|dw:1438436528358:dw|
okay
50+70 is how we got the 120., and we take the ratio of the smaller triangle to the larger one
ratio ?
yea the fraction you saw 50/120 is the ratio
okay.
now the other side of the triangle is 40 on small side and 40+x on larger side
they have to be proportional because they are co-linear so the ratio (that fraction) must be equal
okay.
you can understand that?
i think.
lemme try draw something to show you what i mean|dw:1438437049240:dw|
okay
like this in case the ratio of the triangle is 1:2 or 1/2
its similar as the question you had but the proportion is not so straightforward
so we use the ratio to find the distance of 40+x, with the ratio of the 50/120
I have to go. Can we finish this later ?
sure and see ya!
okay , thank you. i gave you a medal.
thank you
no problem.

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