30 30 60 triangle problem help please ?

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3 Answers

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  • 1 month ago

    A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. 

    The triangle is special because its side lengths are always in the ratio of 1: √3 : 2. 

    Any triangle of the form 30-60-90 can be solved without applying long-step methods such as the Pythagorean Theorem and trigonometric functions.

    30-60-90 triangle:

    If BC = 4, AB =    AC =

  • Jim
    Lv 7
    1 month ago

    If BC = 4:

    4) AB = 4√3

    5) AC = 4*2 = 8

    If AB = 2√3:

    6) BC = AB/√3 = 2√3/√3 = 2

    7) AC = 2 BC = 4

    Using 'a' as in the attached diagram:

    If AB = 9:

    8) √3a = 9

    a = 9/√3

    We prefer to have radical not in the denominator, so multiply by 1 as (√3/√3)

    9/√3 (√/3/√3) = 9√3/3

    a = BC = 3√3

    9) 2a = 2*3√3 = 6√3

    AC = 6√3

    Attachment image
  • 1 month ago

    In a 30-60-90 triangle, the length of the smallest side is half the length of the hypotenuse and the longer length is √3 times the length of the smaller side.

    You are told for #4 and #5 that the smallest side is 4, so:

    AC = 8

    AB = 4√3

    You can use the same rules and logic to do the other four questions.

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