The floor of a pool in the shape of a parallelogram has sides that measure 42 ft and 59 ft. To meet the minimum required length for the shortest​ diagonal, the angles must be 61 degrees and 119 degrees. What is the lengths of the diagonals?

1 Answer
Apr 4, 2018

Angle opposite to shortest​ diagonal is #61^@# which lies in between two sides of lengths #42ft and 59ft#

So using cosine law we get

#"length of shortest diagonal"#

#=sqrt(42^2+59^2-2*42*59*cos61^@)~~53.3ft#

Similarly angle opposite to longest​ diagonal is #119^@# which lies in between two sides of lengths #42ft and 59ft#

So using cosine law we get

#"length of longest diagonal"#

#=sqrt(42^2+59^2-2*42*59*cos119^@)~~87.5ft#