Trig work problem (am I correct?)

AI Thread Summary
The discussion focuses on a trigonometry problem involving the height at which supports cross and the use of similar triangles to express this height in terms of H1 and H2. Participants clarify the proportions related to the height and lengths, with one user correcting the misconception that L is always half of L1. They confirm that the proportions can be rewritten for clarity, suggesting x/H1 = 1 - L/L1 and x/H2 = L/L1. There is confusion about angle bisectors and congruent angles, leading to a correction that not all drawn angles are equal, with specific pairs identified as congruent. The conversation emphasizes the importance of accurately identifying relationships in geometry.
Miike012
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Trig work problem... (am I correct?)

Homework Statement


If we call the height @ which the supports cross ,x, express this height as an equation in terms of H1 and H2 Only... Use similar triangle...

Are my proportion correct?
x/H1 = (L1-L)/L1
x/H2 = (L)/L1 = (L1-L)/L1

Because Where the two lines intersect you can see that the two angles are congruent (If I did it correctly)
Thus L1-L = L


And Are my congruent angles in my picture correct?


Homework Equations





The Attempt at a Solution

 

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Miike012 said:
Because Where the two lines intersect you can see that the two angles are congruent (If I did it correctly)
Thus L1-L = L

(try using the X2 icon just above the Reply box :wink:)

No, that's obviously not correct … you're saying L is always half of L1, which it isn't. :redface:
Are my proportion correct?
x/H1 = (L1-L)/L1
x/H2 = (L)/L1 = (L1-L)/L1

Correct :smile:, but it'll be easier if you rewrite it …

x/H1 = 1 - L/L1
x/H2 = L/L1 …

carry on from there :wink:​
 


tiny-tim said:
(try using the X2 icon just above the Reply box :wink:)

No, that's obviously not correct … you're saying L is always half of L1, which it isn't. :redface:Correct :smile:, but it'll be easier if you rewrite it …

x/H1 = 1 - L/L1
x/H2 = L/L1 …

carry on from there :wink:​


The segment starting from the right starting @ H2 going towards line x has to be the same length as the line segment L1 to x... because isn't line x is a angle bisector...

Thus segment L1-L must equal segment L...?
 
Miike012 said:
… isn't line x is a angle bisector...

Noooo …

draw H1 very small, and you can see that they're not equal! :redface:
 


I see what you are saying but I guess I am confused.. I am just learning geometry so maybe you can help my understand because it states that if an ray bisects an angle.. the ray creates two congruent angles... and a point on the angle bisector is equal distance from the sides of the angle...
 
Yes, but nothing is bisecting anything here.

You've drawn four angles as equal, but they aren't, there's one equal pair, and another equal pair, but the two pairs aren't equal.
 


So my angles that I say are equal are incorrect?
If you can.. can u show me which ones are equal?
 
Miike012 said:
If you can.. can u show me which ones are equal?

Top left and middle right.

Top right and middle left. :smile:
 

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