The table below shows the sum of the sines for triangles per angles A and B. Those for right triangles are bolded, forming a right triangle on the table, except the right side is missing as there's no column for B=90 degrees.  Within that, the represented triangles are acute, and all have values over 2, with a buffer around it of obtuse triangles with sum over 2:

  A B 5   20   35   50   65   80   95  110  125  140  155  170
  5 0.35 0.85 1.30 1.67 1.93 2.07 2.07 1.93 1.67 1.30 0.85 0.35
 10 0.52 1.02 1.45 1.81 2.05 2.16 2.14 1.98 1.70 1.32 0.86
 15 0.69 1.17 1.60 1.93 2.15 2.24 2.19 2.02 1.72 1.32 0.86
 20 0.85 1.33 1.73 2.05 2.24 2.31 2.24 2.05 1.73 1.33 0.85
 25 1.01 1.47 1.86 2.15 2.33 2.37 2.28 2.07 1.74 1.32
 30 1.16 1.61 1.98 2.25 2.40 2.42 2.32 2.08 1.74 1.32
 35 1.30 1.73 2.09 2.34 2.46 2.46 2.34 2.09 1.73 1.30
 40 1.44 1.85 2.18 2.41 2.52 2.49 2.35 2.08 1.72
 45 1.56 1.96 2.27 2.47 2.55 2.51 2.35 2.07 1.70
 50 1.67 2.05 2.34 2.52 2.58 2.52 2.34 2.05 1.67
 55 1.77 2.13 2.39 2.55 2.59 2.51 2.32 2.02
 60 1.86 2.19 2.44 2.57 2.59 2.49 2.28 1.98
 65 1.93 2.24 2.46 2.58 2.58 2.46 2.24 1.93
 70 1.99 2.28 2.48 2.57 2.55 2.42 2.19
 75 2.04 2.30 2.48 2.55 2.52 2.37 2.14
 80 2.07 2.31 2.46 2.52 2.46 2.31 2.07
 85 2.08 2.30 2.44 2.47 2.40 2.24
 90 2.08 2.28 2.39 2.41 2.33 2.16
 95 2.07 2.24 2.34 2.34 2.24 2.07
100 2.04 2.19 2.27 2.25 2.15
105 1.99 2.13 2.18 2.15 2.05
110 1.93 2.05 2.09 2.05 1.93
115 1.86 1.96 1.98 1.93
120 1.77 1.85 1.86 1.81
125 1.67 1.73 1.73 1.67
130 1.56 1.61 1.60
135 1.44 1.47 1.45
140 1.30 1.33 1.30
145 1.16 1.17
150 1.01 1.02
155 0.85 0.85
160 0.69
165 0.52
170 0.35
175