Question

what is tu?
tu =
diagram showing a geometric figure with right angles at t and r, angle at s is 42 degrees, angle between su and sr is 42 degrees, length of ur is 78

Explanation:

Step1: Identify Congruent Triangles

Triangles \( \triangle SUR \) and \( \triangle STU \) are right triangles (right angles at \( R \) and \( T \)) with \( \angle USR = \angle TSU = 42^\circ \) and sharing hypotenuse \( SU \). By AAS (Angle - Angle - Side) congruence, \( \triangle SUR \cong \triangle STU \).

Step2: Determine Corresponding Sides

In congruent triangles, corresponding sides are equal. Side \( UR \) in \( \triangle SUR \) corresponds to side \( TU \) in \( \triangle STU \). Given \( UR = 78 \), so \( TU=UR \).

Answer:

\( 78 \)