SOLUTION: If the sides of a parallelogram and an included angle are 5 ft, 10ft, 100 degrees, respectively, find the length of the shorter diagonal.

Algebra ->  Parallelograms -> SOLUTION: If the sides of a parallelogram and an included angle are 5 ft, 10ft, 100 degrees, respectively, find the length of the shorter diagonal.       Log On


   



Question 1072109: If the sides of a parallelogram and an included angle are 5 ft, 10ft, 100 degrees, respectively, find the length of the shorter diagonal.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
That means each of the other two angles are measure 80 degrees. The shorter diagonal is opposite either of these 80 degree angles.

d for the diagonal
d%5E2=10%5E2%2B5%5E2-2%2A5%2A10%2Acos%2880%29

d=sqrt%28100%2B25-100%2Acos%2880%29%29

d=sqrt%28125-100%2Acos%2880%29%29

highlight%28d=5sqrt%285-4%2Acos%2880%29%29%29