Trigonometry

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!!!!

asked by Becca
  1. 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

    posted by Reiny
  2. 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!!

    posted by Becca
  3. correct conclusion

    posted by Reiny

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