Trigonometry
posted by Becca
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!!!!

Reiny
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 
Becca
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!!

Reiny
correct conclusion
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