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 Acute triangle, Trigonometric function! (Posted on 2007-10-13)
Prove that in an acute triangle sin(A) + sin(B) + sin(C) > 2

 See The Solution Submitted by Chesca Ciprian Rating: 4.0000 (1 votes)

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 not a proof but ... | Comment 1 of 9

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 2.07100 2.04 2.19 2.27 2.25 2.15105 1.99 2.13 2.18 2.15 2.05110 1.93 2.05 2.09 2.05 1.93115 1.86 1.96 1.98 1.93120 1.77 1.85 1.86 1.81125 1.67 1.73 1.73 1.67130 1.56 1.61 1.60135 1.44 1.47 1.45140 1.30 1.33 1.30145 1.16 1.17150 1.01 1.02155 0.85 0.85160 0.69165 0.52170 0.35175`

 Posted by Charlie on 2007-10-13 16:39:03

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