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22 May, 14:15

Each side of a rhombus is 30 units long. One diagonal makes a 25 degree angle with a side. What is the length of each diagonal to the nearest tenth of a unit?

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  1. 22 May, 14:41
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    25.4 units

    54.4 units

    Step-by-step explanation:

    Given that,

    length of each side of rhombus = 30 units

    interior angle = 25 x 2

    = 50°

    other interior angle = (360 - (50x2)) / 2 = 130°

    Formula to use

    c² = a² + b² - ab cosC

    First diagonal

    √ (30² + 30² - 2*30*30*cos 50)

    = 25.35 u

    Second diagonal

    √ (30² + 30² - (2*30*30 * (cos 130)))

    = √ (1800-1800cos130)

    = 54.37 units
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