Question

what is ru?
ru =
(there is a geometric figure with points r, s, t, u. rs is 6, angle at t is 69 degrees, right angles at s and u.)

Explanation:

Step1: Identify Congruent Triangles

Triangles \( RST \) and \( RTU \) are right - angled ( \( \angle RST=\angle RU T = 90^{\circ} \) ), share the side \( RT \), and \( \angle RTS=\angle RTU = 69^{\circ} \). By the Angle - Angle - Side (AAS) congruence criterion, \( \triangle RST\cong\triangle RTU \).

Step2: Determine Length of \( RU \)

Since \( \triangle RST\cong\triangle RTU \), corresponding sides are equal. We know that \( RS = 6 \), and the corresponding side of \( RS \) in \( \triangle RTU \) is \( RU \). So \( RU=RS = 6 \).

Answer:

\( 6 \)