Opposing Triangles: 2 lines cross in shape of "X", bases are parallel

Tyler4550

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Oct 16, 2018
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Hi all -

New to the forum and have a real world problem I am attempting to solve. Apologies ahead of time for the improper use of terminology as math has never been my strong suit.

I have included an image below with the problem I am facing. I need to solve for X. I know I can do it by using the ARCTAN function to find the interior angles where the two triangles meet, then use SIN to ultimately find X. However, is there a more efficient way to solve for X using some sort of principal for triangles that are similar?

Thanks in advance.

Tyler

Hourglass Problem.jpg
 
I have included an image below with the problem I am facing. I need to solve for X. I know I can do it by using the ARCTAN function to find the interior angles where the two triangles meet, then use SIN to ultimately find X. However, is there a more efficient way to solve for X using some sort of principal for triangles that are similar?

Yes, there is an easy way. Because the triangles are similar, corresponding parts are similar. So the ratio of the horizontal sides equals the ratio of the heights. Can you write that proportion, and solve it?

Or, you could just observe that the height of the smaller one is 3 times its base, so the same is true of the larger one.
 
Ha - I'm embarrassed I didn't put that together. What started with ARCTAN and SIN ended up being as simple as X=(ac)/b.

Thanks!

Tyler
 
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