Question #132564

PQ = 6x + 25 and QR = 16 – 3x; Find PR. 


1
Expert's answer
2020-09-14T15:55:39-0400

PR=(6x+25)2+(16−3x)2−2(6x+25)(16−3x)cos(∠PQR)=36x2+300x+625+256−96x+9x2−2(96x−18x2+400−75x)cos(∠PQR)=45x2+204x+881−2(21x−18x2+400)cos(∠PQR).Answer:PR=45x2+204x+881+2cos(∠PQR)(18x2−21x−400)PR=\sqrt{(6x+25)²+(16-3x)²-2(6x+25)(16-3x)cos(\angle PQR)}=\sqrt{36x²+300x+625+256-96x+9x²-2(96x-18x²+400-75x)cos(\angle PQR)}=\sqrt{45x²+204x+881-2(21x-18x²+400)cos(\angle PQR)}. Answer: PR=\sqrt{45x²+204x+881+2cos(\angle PQR)(18x²-21x-400)}


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