Need help

homeschool girl

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The distance from Capital City to Little Village is \(\displaystyle 140\) miles. From Capital City to Mytown is \(\displaystyle 80\) miles, from Mytown to Yourtown is \(\displaystyle 25\) miles, and from Yourtown to Little Village is \(\displaystyle 35\) miles. How far is it from Mytown to Little Village?

here's my diagram:



so far I've figured out that it's impossible for \(\displaystyle \angle C\) to be an obtuse angle but I don't know where to go from there
 

Subhotosh Khan

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The distance from Capital City to Little Village is \(\displaystyle 140\) miles. From Capital City to Mytown is \(\displaystyle 80\) miles, from Mytown to Yourtown is \(\displaystyle 25\) miles, and from Yourtown to Little Village is \(\displaystyle 35\) miles. How far is it from Mytown to Little Village?

here's my diagram:



so far I've figured out that it's impossible for \(\displaystyle \angle C\) to be an obtuse angle but I don't know where to go from there
How did you figure out that \(\displaystyle \angle C\) is NOT an obtuse angle?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
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homeschool girl

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I don't remember exactly what I did but I know I used triangle inequality theorems to prove that the only way for C to be obtuse is if x were negative.
 

Subhotosh Khan

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I don't remember exactly what I did but I know I used triangle inequality theorems to prove that the only way for C to be obtuse is if x were negative.
Was the diagram provided in the assignment? As posted, you may have multiple solutions.

One of the solutions could be that all those points are on one line. → 25+ 35 = 60 and 140 - 80 = 60
 

homeschool girl

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the diagram was not provided, it was just the word problem
 

firemath

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Have you been studying line segment problems?
 
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Subhotosh Khan

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I don't remember exactly what I did but I know I used triangle inequality theorems to prove that the only way for C to be obtuse is if x were negative.
Apply triangle inequality to the diagram you have drawn - and you will see there is only one solution for the length of ML!!
 

homeschool girl

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Apply triangle inequality to the diagram you have drawn
i don't know which one, arent there like 5? all I could figure out is that C is not obtuce but it could be right of acute, and I don't know what Y is
 

Subhotosh Khan

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i don't know which one, arent there like 5? all I could figure out is that C is not obtuce but it could be right of acute, and I don't know what Y is
Sum of (the lengths of any) two sides of a triangle is larger than (or equal to) the (length of the) third side.
 

Dr.Peterson

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The distance from Capital City to Little Village is \(\displaystyle 140\) miles. From Capital City to Mytown is \(\displaystyle 80\) miles, from Mytown to Yourtown is \(\displaystyle 25\) miles, and from Yourtown to Little Village is \(\displaystyle 35\) miles. How far is it from Mytown to Little Village?

here's my diagram:



so far I've figured out that it's impossible for \(\displaystyle \angle C\) to be an obtuse angle but I don't know where to go from there
To make the triangle inequality more tangible, think of it this way: Suppose you have two sticks of length 80 and 140 cm, attached at one end. What is the greatest possible distance between the other ends? Just imagine moving the sticks to accomplish this; what do you see.

Now try to swing them around so the ends are as close as they can possibly be. How are they arranged, and what is that distance?

This gives you a range of possible lengths of ML. Do the same with 25 and 35, and then put the two ranges together.
 

Jomo

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Think straight line like others are pointing out.
 

homeschool girl

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I got x=60.
 

homeschool girl

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I put it in and it was correct, thank you all for your help :)
 
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