The diagonals of a parallelogram are 7 inches and 9 inches respectively they intersect at an angle of 52 degrees Find the sides of the parallelogram?

: Ram P. Tubio

just try drawing it. Often the answers become much clearer with a picture.

For example once you draw the parallelogram with diagonals and angle you will notice that you have a triangle formed by half of each diagonal and one of the sides. You also have the angle where the diagonals meet as part of this triangle.

With 2 known sides (7/2 and 9/2) and a known angle (52 deg) you can find the other side, which is the short side of the parallelogram.

Hopefully you know the law of cosines...

c^2 = a^2 + b^2 - 2ab.cos(C)

c^2 = (7/2)^2 + (9/2)^2 - 2(7/2)(9/2).cos(52)

c^2 = 49/4 + 81/4 - 126/4.cos(52)

c^2 = (49 + 81 - 126.cos(52))/4

c = sqrt(130 - 126.cos(52))/2

c ~= 3.620 inches

Then you just do the same thing again using the supplementary angle, 180-52 = 128.

c = sqrt(130 - 126.cos(128))/2

c ~= 7.204 inches