Trigonometry

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PLEASE HELP!! I really don't understand this...I just started learning about trigonometry and SOH CAH TOA and I think this probably has to do with that but I don't know how to apply it... Please explain this to me!!!! I need to know how to do it and not just the answer.

Triangle ABC has m<b = 54 degrees, b = 20cm, and a = 30cm. How many triangles are defined by these measures?

A. 0

B. 1

C. 2

D. not enough information


Thank you so much!!!!

  • Trigonometry -

    Your probably made a sketch and have learned the sine law
    If not, go to the construction part of my reply

    using the sine law:

    sinA/30 = sin54/20
    sinA = 1.2135....

    but that is not possible , since the sine of any angle has to be between -1 and 1
    So there is no such triangle possible

    OR

    You might have been able to make a sketch, but when you actually attempt to draw this triangle, it can't be done.

    Draw a base of 30 cm, (this will be BC)
    use your protractor to draw angle B = 54 degrees, mark off AB and extend it some distance.
    Set your compass at 20 cm, put your compass at C and draw an arc.
    A would be the intersection of that arc and BA.
    BUT as you will see it does not reach BA
    Thus no triangle is possible

  • Trigonometry -

    Ohhh I think I understand!! So that means that the answer would be 0, since no triangle is possible?? Thank you so much for explaining this to me!!

  • Trigonometry -

    correct conclusion

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