Two adjacent sides of a parallelogram are 11 cm and 23 cm long, and the ratio of the lengths of its diagonals is 2:3. Find the lengths of the diagonals of this parallelogram.
#Two adjacent sides of a parallelogram are 11 cm and 23 cm long, and the ratio of the lengths of its
twin citrus
queen meadow
Two adjacent sides of a parallelogram are 11 cm and 23 cm long, and the ratio of...
(2x)² = 11² + 23² - 2(11)(23)cos(ø)
(3x)² = 11² + 23² - 2(11)(23)cos(180 - ø)
solve both equations to get x, and the diagonals are 2x and 3x
twin citrus
(2x)² = 11² + 23² - 2(11)(23)cos(ø)
(3x)² = 11² + 23² - 2(11)(23)cos(180 - ø)
so...
Thank you very much. I have a question, how to get cos(ø)?
old sleetBOT
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queen meadow
Thank you very much. I have a question, how to get cos(ø)?
cos(180 - ø) = -cos(ø)
urwelcome
twin citrus
(2x)² = 11² + 23² - 2(11)(23)cos(ø)
(3x)² = 11² + 23² - 2(11)(23)cos(180 - ø)
so...
(2x)² = 11² + 23² - 2(11)(23)cos(ø), this one will be x = 6?
(3x)² = 11² + 23² - 2(11)(23)cos(180 - ø), and this x = 4?
queen meadow
(2x)² = 11² + 23² - 2(11)(23)cos(ø), this one will be x = 6?
wdym? you should solve both equations to get x, either by using elimination/substitution
twin citrus
Ohh, I got it, thank you again