Help with Trigonometry: Combine Two Triangles

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The discussion centers on the geometric relationship between two triangles: a red triangle with sides a=1.25, b=4.5, c=4.67, and a larger triangle with sides a=98.75, b=20.5, c=100.85. The user seeks clarification on why combining these triangles does not yield the original dimensions of the main triangle. A key insight reveals that the triangles are not similar due to differing height-base ratios, specifically that 1.25/4.5 does not equal 25/100. This discrepancy indicates a fundamental misunderstanding of triangle similarity principles.

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Hello Gys

I have new question for you today... if u ready, let's begin



http://www.mediafire.com/view/?2pp4u074ppijfbt

we have two triangles, the main one is the blue the secondary is the red.

if we divide the main triangle into two triangles we will get

The red triangle a=1.25, b=4.5 and c=4.67

The new triangle will be a=100-1.25=98.75, 25-4.5=20.5 so c=sqrt((98.75)^2+(20.5)^2) ===> c=100.85

===========================
Now we have two triangles
1- a=1.25, b=4.5 and c=4.67
2- a=98.75, b=20.5 and c=100.85

The question is there is some thing missing because when we want to combine the two triangles again suppose we get same length's of the the main triangles ( blue triangles ).

Any one could get the point ??

Tnx all
 

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hgphtgi said:
Hello Gys

I have new question for you today... if u ready, let's begin



http://www.mediafire.com/view/?2pp4u074ppijfbt

we have two triangles, the main one is the blue the secondary is the red.

if we divide the main triangle into two triangles we will get

The red triangle a=1.25, b=4.5 and c=4.67

The new triangle will be a=100-1.25=98.75, 25-4.5=20.5 so c=sqrt((98.75)^2+(20.5)^2) ===> c=100.85

===========================
Now we have two triangles
1- a=1.25, b=4.5 and c=4.67
2- a=98.75, b=20.5 and c=100.85

The question is there is some thing missing because when we want to combine the two triangles again suppose we get same length's of the the main triangles ( blue triangles ).

Any one could get the point ??

Tnx all

Things are really fouled up in the drawing. From appearances, the small triangle and large triangle are similar, but it looks like the height and base of the small triangle have been switched. Assuming the base of the small triangle is really 4.5 and the height is really 1.25, the triangles are not similar, since their height-base ratios are different (1.25/4.5 ≠ 25/100).

If the base of the small triangle happened to be 5, then the two triangles would be similar.
 
Last edited by a moderator:

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