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

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 (:

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  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

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