What is PC? Please explain how did you work it out.

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1 Answer
CW
Jan 7, 2018

#PC=33.0# cm

Explanation:

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given #angleAPB=angleBPC=angleCPA#,
#=> angleAPB=angleBPC=angleCPA=360/3=120^@#
Use the law of cosines to find #AB#,
#AB^2=AP^2+PB^2-2*AP*PB*cos120#
#=> AB^2=10^2+6^2-2*10*6*cos120=196#,
#=> AB=14#
let #angleABP=x#,
#=> sinx/(AP)=sin120/(AB), => x=sin^-1((10*sin120)/(14))=38.213^@#
draw a line #PD#, perpendicular to #BC#,
#=> angleBPD=angleABP=38.213#
#=> PD=PBcos38.213=6*cos38.213=4.714#,
#=> angleDPC=angleBPC-angleBPD=120-38.213=81.787^@#
#=> PC=(PD)/cos81.787=4.714/cos81.787~~33.0 "cm"#

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