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Two sides of a parallelogram are 20 and 30 and the included angle is 36 degrees. Find the length of the longer diagonal.

 Jan 4, 2015

Best Answer 

 #1
avatar+128079 
+5

 

 

 

 

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

 

 Jan 4, 2015
 #1
avatar+128079 
+5
Best Answer

 

 

 

 

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

 

CPhill Jan 4, 2015

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