Two sides of a parallelogram are 20 and 30 and the included angle is 36 degrees. Find the length of the longer diagonal.
Since opposite angles of a paralleogram are supplemental, the other included angle between the sides is given by (180 - 36) = 144°
And the length of the longer diagonal - call it "D" - will be opposite this angle......and we can find this using the Law of Cosines...so we have
D^2 = 30^2 + 20^2 - 2(20)(30)cos(144)
D^2 = 2270.82039325 take the square root of this
D = about 47.65 units
Since opposite angles of a paralleogram are supplemental, the other included angle between the sides is given by (180 - 36) = 144°
And the length of the longer diagonal - call it "D" - will be opposite this angle......and we can find this using the Law of Cosines...so we have
D^2 = 30^2 + 20^2 - 2(20)(30)cos(144)
D^2 = 2270.82039325 take the square root of this
D = about 47.65 units