SOLUTION: One diagonal of a parallelogram is 16.5 it makes angles of 36�10' and 14�30' respectively with the sides. Find the sides.

Question 1108438: One diagonal of a parallelogram is 16.5 it makes angles of 36�10' and 14�30' respectively with the sides. Find the sides.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Here is a sketch of the parallelogram, with sides of length and ,
and a diagonal of length 16.5.
The diagonal divides the parallelogram into two triangles
whose angles measure , and .

Applying Law of Sines to the triangle with the angles and sides labeled, we get

A calculator tells us that accurate to 6 decimal places:

and

.
Substituting those values,

Solving the equations

and

,
we get values for and .
Calculated to 2 decimal places, the lengths are:

and

.
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