Trig work problem (am I correct?)

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Homework Help Overview

The discussion revolves around a trigonometry problem involving similar triangles and angle bisectors. The original poster is attempting to express a height in terms of other variables and is questioning the correctness of their proportions and angle relationships.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster presents proportions related to heights and lengths, questioning their correctness. They also inquire about the congruence of angles in their diagram. Other participants engage by confirming some proportions while challenging the assumptions about angle bisectors and congruence.

Discussion Status

Participants are actively exploring the relationships between angles and lengths, with some guidance provided on rewriting proportions. There is a mix of agreement and disagreement regarding the correctness of the original poster's assumptions about angle congruence.

Contextual Notes

The original poster is learning geometry and is navigating through concepts of angle bisectors and congruence, indicating a potential gap in understanding these principles. The discussion reflects varying interpretations of the geometric setup.

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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