Question

what is uv? uv = \boxed{} submit

Explanation:

Step1: Identify the Angle Bisector

Since \( \angle UTS \) is split into two \( 60^\circ \) angles by \( TV \), \( TV \) is the angle bisector. Also, \( UV \perp UT \) and \( SV \perp ST \), so by the Angle - Bisector Theorem, the distances from a point on the angle bisector to the two sides of the angle are equal. That is, \( UV = SV \).

Step2: Determine the Length of \( UV \)

We are given that \( SV = 33 \). From the Angle - Bisector Theorem (the property of angle bisectors in a right - angled context, where the perpendicular distances from a point on the angle bisector to the two legs of the angle are equal), we know that \( UV=SV \).

Answer:

\( 33 \)