SOLUTION: Two side of a parallelogram are 694 feet and 418 feet
respectively, one diagonal is 602 feet. Find the length
of the other diagonal.
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-> SOLUTION: Two side of a parallelogram are 694 feet and 418 feet
respectively, one diagonal is 602 feet. Find the length
of the other diagonal.
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Question 1019495: Two side of a parallelogram are 694 feet and 418 feet
respectively, one diagonal is 602 feet. Find the length
of the other diagonal. Found 2 solutions by Edwin McCravy, ikleyn:Answer by Edwin McCravy(20054) (Show Source):
We will be using the law of cosines.
Since the adjacent interior angles of a parallogram are
supplementary, cos(∠ABC) = -cos(∠DAB), so
Using the law of cosines on ΔABD
BD² = AD² + AB² - 2∙ AD∙ AB∙cos(∠DAB)
(1) 602² = 418² + 694² - 2∙418∙694∙cos(∠DAB)
Using the law of cosines on ΔABC
AC² = BC² + AB² - 2∙ BC ∙AB∙cos(∠ABC)
AC² = 418² + 694² - 2∙418∙694∙[-cos(∠DAB)]
(2) AC² = 418² + 694² + 2∙418∙694∙cos(∠DAB)
Adding equations (1) and (2)
(1) 602² = 418² + 694² - 2∙418∙694∙cos(∠DAB)
(2) AC² = 418² + 694² + 2∙418∙694∙cos(∠DAB)
602² + AC² = 2∙418² + 2∙694²
AC² = 2∙418² + 2∙694² - 602²
AC² = 2∙418² + 2∙694² - 602²
AC² = 349448 + 963272 - 362484
AC² = 950316
AC = √950316
AC = 974.8415256 ft.
Edwin
You can put this solution on YOUR website! .
Two side of a parallelogram are 694 feet and 418 feet
respectively, one diagonal is 602 feet. Find the length
of the other diagonal.
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You can get the solution quickly, if you apply this property of a parallelogram diagonals:
Let a, b, c and d be the lengths of the sides of a parallelogram and and be the lengths of its diagonals.
Then = = .
