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Answer to Question #34177 in Geometry for Ranjit

Question #34177
Gadongville and Ledesma Subdivision are two villages located on opposite sides of an island. Hacienda Alcayde is located well away in the island and has a straight highway connection to each village. It is 84.6 miles from Gadongville to Hacienda Alcayde and 33.8 miles from Hacienda Alcayde to Ledesma Subdivision. A surveyor notes that the highway from Ledesma Subdivision to Hacienda Alcayde makes an angle measure of 63°20¢ with the line of sight from Ledesma Subdivision to Gadongville. How far apart are the two villages?
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