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Distance between two lighthouses PQ = 3 mi
\Distance from lighthouse P to ship x = ?
\Distance from lighthouse Q to ship y = ?
\Distance from ship to shore z = ?
\Let distance from lighthouse P to point at ship center makes right angle = k
\From Upper Right angled triangle
\z = k /tan15
\From Lower Right angled triangle
\z = ( 3 - k ) / tan35
\k / tan15 = ( 3 - k ) / tan35
\ktan35 = 3tan15 – ktan15
\k (tan35 – tan15 ) = 3 tan15
\k = 3 tan15 / (tan35 – tan15
\k = 1.86
\From Upper Right angled triangle
\z = k /tan15
\z = 1.86 /tan15
\z = 6.94 mi
\![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
Distance from ship to shore is 6.94 miles
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