+90 The diagonals of a parallelogram are 18 cm and 28 cm respectively. One of the sides of the parallelogram is 10 cm.
A. Compute the smallestangle of intersection of the two diagonals
B. Compute the area of the parallelogram
C. Compute the other side of the parallelogram
+130081
A. Since the diagonals of a parallelogram bisect each other, we can use the Law of Cosines to find one of the intersecting angles of the diagonals.....
So we have
!0^2 = 14^2 + 9^2 - 2(14)(9)cosΘ simplify
100 = 196 + 81 - 252 cosΘ
cosΘ = (100-196 - 81) / (-252) = 0.7023809523809524
And, using the cosine inverse to find Θ, we have
cos-1 ( 0.7023809523809524) = about 45.381658347154° ... and this is the smaller angle
B. The larger angle of the intersecting diagonals is given by (180 - 45.381658347154) = 134.618341652846°
And the total area of the parallelogram is given by (14)(9)(sin 45.381658347154 + sin 134.618341652846) = 179.373911146416 sq cm
C. Using the Law of Cosines we can find the length of the other side...call this "S"
S^2 = 14^2 + 9^2 - 2(14)(9)cos(134.618341652846)
S^2 = 454.000000000012 .... take the square root of both sides
S = about 21.3 cm
+130081
A. Since the diagonals of a parallelogram bisect each other, we can use the Law of Cosines to find one of the intersecting angles of the diagonals.....
So we have
!0^2 = 14^2 + 9^2 - 2(14)(9)cosΘ simplify
100 = 196 + 81 - 252 cosΘ
cosΘ = (100-196 - 81) / (-252) = 0.7023809523809524
And, using the cosine inverse to find Θ, we have
cos-1 ( 0.7023809523809524) = about 45.381658347154° ... and this is the smaller angle
B. The larger angle of the intersecting diagonals is given by (180 - 45.381658347154) = 134.618341652846°
And the total area of the parallelogram is given by (14)(9)(sin 45.381658347154 + sin 134.618341652846) = 179.373911146416 sq cm
C. Using the Law of Cosines we can find the length of the other side...call this "S"
S^2 = 14^2 + 9^2 - 2(14)(9)cos(134.618341652846)
S^2 = 454.000000000012 .... take the square root of both sides
S = about 21.3 cm
