SOLUTION: A certain city block is in the form of a parallelogram. Two of its sides measure 82 ft. and 25 ft. If the area of the land in the block is 1,467 sq. ft., what is the length of the

Algebra ->  Parallelograms -> SOLUTION: A certain city block is in the form of a parallelogram. Two of its sides measure 82 ft. and 25 ft. If the area of the land in the block is 1,467 sq. ft., what is the length of the       Log On


   

Question 1150859: A certain city block is in the form of a parallelogram. Two of its sides measure 82 ft. and 25 ft. If the area of the land in the block is 1,467 sq. ft., what is the length of the shorter diagonal?
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the formula  S = a%2Ab%2Asin%28alpha%29  for the area of a parallelogram,

where "a" and "b" are any two adjacent side lengths and alpha  is the concluded angle between them.


From the formula,


    sin%28alpha%29 = 1467%2F%2882%2A25%29 = 0.71561.


Then  cos%28alpha%29 = sqrt%281-sin%5E2%28alpha%29%29 = sqrt%281-0.71561%5E2%29 = 0.6985.


     Notice that for the shorter diagonal, we choose the positive sign of  cos%28alpha%29.


Now apply the cosine law.


The shorter diagonal is  sqrt%28a%5E2+%2B+b%5E2+-+2abcos%28alpha%29%29.


Substitute the data and calculate the numerical value on your own.