Triangle relationship

Theta 1 and theta 2 are angles in two right triangles with different heights but the same base. The goal is to prove the relationship between these angles. The current proof is through circle theorems, but an algebraic proof is desired. The relationship is shown to be that tan(theta 1) = 2tan(theta 2).
  • #1
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There are two right triangles, the first one with the base a and the height h. The second has the base a and 2h. The question is to prove the relationship between the theta 1 and theta 2 angles in the triangles (see attachment). I have been able to prove it with circle theorems but not with algebra, so i would appreciate if someone could deliver a algebraic proof, thank you.
 

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  • #2
Well, you should have:
[tex]tan(\theta_{1})=\frac{a}{h}=2\frac{a}{2h}=2tan(\theta_{2})[/tex]
 
  • #3
follow up

Does this mean theta 1 is twice as big as theta 2?
 
  • #4
Link said:
Does this mean theta 1 is twice as big as theta 2?
In general, No. However, it is approximatly true when h>> a.
 

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