In a triangle with angles \( T = 26^\circ \) and \( U = 64^\circ \), the third angle \( V \) can be found using the fact that the sum of angles in a triangle is \( 180^\circ \):
\[ V = 180^\circ - T - U = 180^\circ - 26^\circ - 64^\circ = 90^\circ \]
Since triangle \( TUV \) contains a right angle (90 degrees), we can apply the Pythagorean theorem. In a right triangle, the Pythagorean theorem states that:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the side opposite the right angle), and \( a \) and \( b \) are the lengths of the other two sides.
To express this in terms of angles, let’s assume:
- Side opposite angle \( T \) is \( t \)
- Side opposite angle \( U \) is \( u \)
- Hypotenuse (opposite angle \( V \)) is \( v \)
Then, from the Pythagorean theorem, we have:
\[ t^2 + u^2 = v^2 \]
Thus, the relationship among the sides in this right triangle based on the Pythagorean theorem is:
\[ t^2 + u^2 = v^2 \]