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Help me I am lost? I do not even know where to start:
The shorter leg of a 30°–60°–90° triangle is 12. What are the lengths of the longer leg and the hypotenuse, to the nearest tenth?

  • math -

    First, draw your triangle so you can see what you're doing. The short side, 12, will be opposite the small angle, 30.

    We know that the sin of an angle = opposite over hypotenuse. The angle is 30, and we can look up sin(30)=0.5.

    So opposite (which we know is 12) over hypotenuse = 1/2.

    12/hypotenuse = 1/2
    hypotenuse = 24.

    Now we can get the final, adjacent, side in either of two ways:

    1. Pythagoras: 12^2 + adjacent^2 = 24^2

    or

    2. use the definition of cos = adjacent over hypotenuse. We can look up cos(30) = sqrt(3)/2 or .8660. So:
    adjacent/24 = .8660

    and mutiply across from there.

  • math -

    The sides of the 30-60-90 triangel are in the ratio of 1:√3:2

    your triangle is 12:a:b

    so 1/12 = √3/a
    a = 12√3

    and 1/12 = 2/b
    b = 24
    the other two sides are 12√3 and 24

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