Hello unknown008.

PQR is an equilateral triangle PR =1 T is on QR . A line fromT to PQ is drawn perpendicular to that line meeting it @S ST =TR What length is ST?

By inspection the various angles are

QTS =30 STR=150 TRS=15 PSR=75 PRS=45 SPR= 60

Use the sine rule

1/sin75= SR/sin60 SR=0.897

0.897/sin150= ST/sin15 ST = 0.4643

bjh