hi I reposted this question to see if I would get the answer the person who posted this one last time says that 9sqrt3 is wrong (and I check if they were right) do here is the question again

Question

Given: ∆PQR, m∠R = 90°
m∠PQR = 75°
M ∈ PR (meaning that m in on segment PR) , MP = 18
m∠MQR = 60°
Find: RQ

Thanks (:

Answer 1

I made your sketch and filled in all the angles .
From triangle MPQ
QM/sin15 = 18/sin60
QM = 18sin15/(√3/2) = 16sin15/√3

in triangle RMQ
cos15 = QR/QM
QR = QM cos15
= (36sin15)/√3 * cos15
= 18(2sin15cos15)/√3
= 18(sin30)/√3
= 18(1/2) / √3
= 9/√3
= 9/√3 * √3/√3
= 9√3 /3
= 3√3