math (geometry)

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find the perimeter of a 30-60-90 degree triangle whose shorter leg is 16 cm

  • math (geometry) -

    The shorter leg is adjacent to the 60° angle.
    We know from trigonometry that
    sin 60° = 1/2
    tan 60° = √3
    Therefore:
    adjacent side, A = 16 cm
    opposite side, O = 16 tan 60° = 16√3
    hypotenuse, H = 16 /sin 60° = 32
    The perimeter is the sum of the three sides, namely
    perimeter = A+O+H=16(3+√3)

  • math (geometry) -

    A 30-60-90 triangle has sides 1, √3 and 2 for a perimeter of 3+√3

    since the shorter side of your triangle is 16, the perimeter must be 16 times as large or 48 + 16√3

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