+90 The sides of a rhombu is 100 cm long and the length of the longer diagonal is 160 cm.
a. Find the smaller angle between the sides ofthe rhombus.
b. Find the length of the smaller diagonal.
c. Find the area of the rhombus.
+128407 a. We can use the Law of Cosines to find the larger angle "Θ" between the sides...we have
160^2 = 100^2 + 100^2 - 2(100)(100)cosΘ simplify
cosΘ = 5600/(-2*100^2) = -7/25 ... find Θ by using the cosine inverse..
cos-1(-7/25) = about 106.26°
And since adjacent angles in a rhombus are supplementary, the smaller angle between the sides = (180-106.26)= 73.74°
b. We can again use the Law of Cosines to find the length of the smaller diagonal.....call it "D"....so we have
D^2 = 100^2 + 100^2 - 2(100)(100)cos(73.74) = 14400.06859844 .. take the square root of this
D = about 120
c. The area is given by (1/2) the product of the diagonals = (1/2)(160)(120) = 9600 sq units
+128407 a. We can use the Law of Cosines to find the larger angle "Θ" between the sides...we have
160^2 = 100^2 + 100^2 - 2(100)(100)cosΘ simplify
cosΘ = 5600/(-2*100^2) = -7/25 ... find Θ by using the cosine inverse..
cos-1(-7/25) = about 106.26°
And since adjacent angles in a rhombus are supplementary, the smaller angle between the sides = (180-106.26)= 73.74°
b. We can again use the Law of Cosines to find the length of the smaller diagonal.....call it "D"....so we have
D^2 = 100^2 + 100^2 - 2(100)(100)cos(73.74) = 14400.06859844 .. take the square root of this
D = about 120
c. The area is given by (1/2) the product of the diagonals = (1/2)(160)(120) = 9600 sq units
