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.

Algebra ->  Parallelograms -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a sketch of the parallelogram, with sides of length x and y ,
and a diagonal of length 16.5.
The diagonal divides the parallelogram into two triangles
whose angles measure red%28%2236+%B0+10+%27+%22%29 , red%28%2214%B030%27+%22%29 and red%28A%29 .


Applying Law of Sines to the triangle with the angles and sides labeled, we get
16.5%2Fsin%28red%28A%29%29%22=%22x%2Fsin%28red%28%2236+%B0+10+%27+%22%29%29%22=%22y%2Fsin%28red%28%2214%B030%27+%22%29%29
%2240%27%22=129%5Eo%2220%27%22
A calculator tells us that accurate to 6 decimal places:
sin%28red%28A%29%29%22=%22%22sin+%28%22129%5Eo%2220%27+%29%22%22=%220.773472 ,
%22sin+%28%2236%5Eo%2210%27+%29%22%22=%220.590136 and
%22sin+%28%2214%5Eo%2230%27+%29%22%22=%220.250380 .
Substituting those values,
16.5%2F0.773472%22=%22x%2F0.590136%22=%22y%2F0.250380
Solving the equations 16.5%2F0.773472%22=%22x%2F0.590136 and 16.5%2F0.773472%22=%22y%2F0.250380 ,
we get values for x and y .
Calculated to 2 decimal places, the lengths are:
x%22=%2216.5%2A0.590136%2F0.773472%22=%2212.59 and
y%22=%2216.5%2A0.250380%2F0.773472%22=%225.34 .