∆SQT is isosceles (SQ=TQ=20) and, since ∠QST=∠QTS=30°, ST=20√3.
∠R=20°, so one of the other angles of ∆RST must be 90°.
Let ∠RST=90°, then ∠RSQ=90-30=60°.
ST/RS=tanR, so RS=STcotR=20√3cot(20)=95.1754.
From the Cosine Rule:
RQ²=RS²+SQ²-2RS.SQcosRSQ,
RQ²=1200cot²(20)+400-400√3cot(20)cos(60),
RQ²=9058.3586+400-1903.5082,
RQ²=7554.8504,
RQ²=86.92, 86.9 to 1 decimal place.