All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Acute triangle, Trigonometric function! (Posted on 2007-10-13) Difficulty: 3 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts 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 2.07
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

  Posted by Charlie on 2007-10-13 16:39:03
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information