SOLUTION: The diagonals of a rectangle are 11 cm long and intersect at a 60 degree angle. How do you find the dimensions of the rectangle?

 
Since the diagonals of a rectangle are both equal in length and bisect
each other, the line segments AC and BC are equal to half of 11 cm, or
5.5 cm each. That makes triangle ABC isosceles, and therefore the base 
angles are equal and since they have to be 60° each, that means that 
triangle ABC is not only isosceles but also equilateral.  Therefore 
side AB is also 5.5 cm. So we have one dimension of the rectangle 
immediately as 5.5 cm.  To get the other dimension, draw a line from
C perpendicular to AB. Label the point D where it touches AB



Since CD bisects AB, AD's length is half of 5.5 cm or 2.75 cm. Also
CD is one-half the height of the rectangle. 

Now since triangle ACD is a right triangle we can use the Pythagorean
theorem to find CD, which is half the height of the rectangle:













So the height of the rectangle is twice CD.  

Therefore the height is 9.526279442 cm.

So the dimensions of the rectangle are 5.5 cm x 9.526 cm.,
approximately.

Edwin