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After a violent storm a 34 foot mast snapped in two, and the upper part fell with the top hitting the ground 10 feet from the foot of the mast.
\n" ); document.write( " The upper part had not completely broken off. How much of the mast is still above the deck and what is the length of the portion that has fallen to the deck?
\n" ); document.write( ":
\n" ); document.write( "Let m = portion of the mast that remains vertical
\n" ); document.write( "Let d = portion of the mast that fell to the deck
\n" ); document.write( ":
\n" ); document.write( "Originally a 34' mast, therefore:
\n" ); document.write( "m + d = 34
\n" ); document.write( "d = (34-m)
\n" ); document.write( ":
\n" ); document.write( "This forms a right triangle where:
\n" ); document.write( "d = the hypotenuse
\n" ); document.write( "m = one leg
\n" ); document.write( "10 = the other leg
\n" ); document.write( ":
\n" ); document.write( "d^2 = m^2 + 10^2
\n" ); document.write( "d^2 = m^2 + 100
\n" ); document.write( "replace d with (34-m)
\n" ); document.write( "(34-m)^2 = m^2 + 100
\n" ); document.write( "FOIL
\n" ); document.write( "1156 - 68m + m^2 = m^2 + 100
\n" ); document.write( "Combine like terms
\n" ); document.write( "-68m + m^2 - M^2 = 100 - 1156
\n" ); document.write( "-68m = -1056
\n" ); document.write( "m =
\n" ); document.write( "m = +15.53 ft is what's left of the mast
\n" ); document.write( "then
\n" ); document.write( "d = 34 - 15.53
\n" ); document.write( "d = 18.47 ft fell to the deck
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this in a calc: enter