a geometry question..?

Question

in an acute triangle ABC, if tanA=t-1,tanB=t+1, so what's the value range of t?

Answer 1

"it is an acute triangle" if and only if "tanA>0&tanB>0&tanC>0";
so t-1>0;t+1>0;
so t>1 at least .
what about C?
tan(180deg-C)=tan(A+B)=(tanA+tanB)/(1-tanA*tanB)
=(t-1+t+1)/(1-(t*t-1))=-2/t (always <0 when t>1)
so tanC always >0 when t>1
so the result is (t>1)or(1,+infinity).

Answer 2

In an acute triangle, all angles must have positive tangent, so we need t > 1.

However, there's no upper limit to t. As t gets large, A and B will both grow close to 90° and C will grow small, but ABC will still be an acute triangle. So the range of t is (1, ∞).

e.g. if t = 100 then angle A ≈ 89.421° and angle B ≈ 89.433°, so angle C ≈ 1.146°.

Answer 3

sorry man - what's an acute triangle? achh! don't worry - I found a definition where none of the interior angles is > 90 degrees (pi/2).