How many Triangles are possible with these dimensions?

Question

In triangleJKL, j= 38mm k=32mm and angle J= 107 degrees. How many Triangles are possible with these dimensions?

Please explain your process.

Thank you

Answer 1

107 degrees is the angle opposite side j = 38mm, the longest side

total angles sum to 180. 107 is greater than 180/2=90, so it's impossible for angle K or angle L to be greater than angle J. 38mm is necessarily the longest side. 32 and side l are the smaller sides.

Use the law of sines to calculate angle K. sin107/38 = sinK/32. Once you know K then L = 180-107-K, that gives you all 3 angles. then sinL/l = sin107/38 gives side l, giving all 3 angles and sides

K=53.64 degrees, L= 19.36 degrees J=107 degrees

k= 32, l = 13.17mm, j= 38mm

Just one possible triangle sides 38, 32, 13.17