SOLUTION: Triangle ABC contains side lengths b = 3 inches and c = 5 inches. In two or more complete sentences describe whether or not it is possible for m < B = 45°.

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Question 1054093: Triangle ABC contains side lengths b = 3 inches and c = 5 inches. In two or more complete sentences describe whether or not it is possible for m < B = 45°.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!




In the above drawing, each of the tic-marks are equal and
represent 1 inch each.  The angle B has measure 45°.  We can
see by the arc that the line AC, which equals 3 inches, is 
not long enough to reach the slanted side of the 45° angle.
Therefore triangle ABC is not possible.  We can also show
by the law of sines that no triangle ABC with the given
properties in possible.

b%2Fsin%28B%29=c%2Fsin%28C%29

b%2Asin%28C%29=c%2Asin%28B%29

sin%28C%29=%28c%2Asin%28B%29%29%2Fb

sin%28C%29=%285%2Asin%28%2245%B0%22%29%29%2F3

sin%28C%29=%221.178511302%22

Since sines of angles are always less than one, this shows
that there is no possible way to have an angle C.  Therefore
it is impossible to have a triangle ABC with the given
properties.

Edwin