Question

in \\( \triangle ty k \\), \\( ty > tk \\) and \\( yk < tk \\). if one of the angles in \\( \triangle ty k \\) is obtuse, which angle is it?

Explanation:

Step1: Recall the side - angle relationship in a triangle

In a triangle, the larger side is opposite the larger angle. Given \(TY> TK\) and \(YK < TK\), we can order the sides as \(TY> TK> YK\).

Step2: Determine the largest angle

Since \(TY\) is the longest side, the angle opposite \(TY\) (which is \(\angle K\)) is the largest angle.

Step3: Identify the obtuse angle

If one angle is obtuse (greater than \(90^{\circ}\)), and it is the largest angle in the triangle. Because the largest angle in a triangle with side lengths \(TY> TK> YK\) is \(\angle K\), so \(\angle K\) is the obtuse angle.

Answer:

\(\angle K\)