How Do Theta 1 and Theta 2 Relate in Different Right Triangles?

AI Thread Summary
The discussion centers on the relationship between the angles theta 1 and theta 2 in two right triangles with the same base but different heights. The first triangle has a height of h, while the second has a height of 2h. An algebraic proof is sought to establish the relationship, with a reference to the tangent function showing that tan(theta 1) equals twice tan(theta 2). However, it is clarified that theta 1 is not necessarily twice as large as theta 2, though this approximation holds true when the height h is significantly greater than the base a. The conversation emphasizes the need for a rigorous algebraic proof to fully understand the angle relationship.
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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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Well, you should have:
tan(\theta_{1})=\frac{a}{h}=2\frac{a}{2h}=2tan(\theta_{2})
 
follow up

Does this mean theta 1 is twice as big as theta 2?
 
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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