Question

given a right triangle with an acute angle, if tangent angle = cotangent angle what would this triangle look like

Answer 1

a 45-45-90 triangle?

Answer 2

tan(x) = opp/adj

cot(x) = adj/opp


So if tan(x) = cot(x), then


opp/adj = adj/opp

opp^2 = adj^2

opp = adj


which means that this triangle has legs that are equal in length. So you would have a 45-45-90 degree triangle.

Answer 3

Looking at the drawing,
\[\tan(x)=\frac{a}{b}\]
\[\cot(x)=\frac{b}{a}\]

since \[\tan(x)=\cot(x)\]
\[\frac{a}{b}=\frac{b}{a}\]
simplify, so \[a^2=b^2\]
so \[a=b\]
The legs of the triangle are the same length

By numerous properties and definitiongs that you've already learned, since the legs of the right triangle are the same length, then the acute angles are the same, and this happens only in a 45-45-90 triangle