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a parallelogram has sides of lengths 9 and 8, and one angle is 45°. find the lengths of the diagonals. (round your answers to two decimal places. enter your answers as a comma-separated list.)

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mhanifa

Answer:

  • 6.57 units; 15.71 units

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Let the diagonals be d₁ and d₂.

One of the diagonals has opposite angle 45° and the other one- 135° since adjacent angles of a parallelogram add to 180°.

Use the law of cosines to find diagonals.

Find d₁:

  • [tex]d_1=\sqrt{8^2+9^2-2*8*9*cos(45 deg)} =\sqrt{43.18} =6.57\ rounded[/tex]

Find d₂:

  • [tex]d_2=\sqrt{8^2+9^2-2*8*9*cos(135 deg)} =\sqrt{246.82} =15.71\ rounded[/tex]

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