00:01
In this problem we have given a parallelogram has side lengths of 6 and 4 and also we have provided that one angle is 47 degrees.
00:12
Now we have to find the length of smaller diagonal as well as the length of longer diagonal.
00:19
So let's suppose this is the we can say parallelogram and we can name it as say a b, c and d.
00:32
And let's suppose this is the angle which is 47 degree and if this is 47 degree opposite would be the same angle.
00:41
So here this would be 47 degrees.
00:43
Now we can find the remaining angles like say this would be 180 degree and this would be minus 47 degree is equal to 133 degrees.
00:59
So this would be equals to 133 degrees.
01:03
And this angle would be again 138 degrees now we can say here diagonal ac would be the longer diagonal from this figure and bd would be the shorter diagonal and similarly we can say a b side would be 6 and this would be 6 and this would be equals to 4 and this would be 4 and from the property of parallel we know that the diagonals of the parallelogram intersect at right angle.
01:35
So this would be here right angle, this is here right angle.
01:41
And let's suppose this is intersecting at point o.
01:44
So here we can say oa square plus this would be ob square is equal to 6 square.
01:54
And also in this triangle, so we can say in a triangle oab, we can say oa b, we can say oa is equal to this would be ab and cost 47 divided with 2, 47 degree divided with 2.
02:08
So ab is equal to 6 and cost this term is equal to 0 .909...