• Support PF! Buy your school textbooks, materials and every day products Here!

Question from trigonometry -- prove that the largest angle is greater than 120°

  • #1
Thread moved from the technical forums, so no HH Template is shown.
In a triangle whose sides are 3,4 and root 38 metres respectively, prove that the largest angle is greater than 120°
  • My answer: Here angle C > B.....(1) and C > A ......(2) adding (1) and (2) we get 2c > A+B, taking sine both side , sin2C = sin(A+B) = sin(C), therefore cosc > (1/2) therefore angle C> 60°
  • I am not getting C> 120°, what is the problem please help
 

Answers and Replies

  • #2
(180-60)=120 is also a solution, now you should think how to prove that particular solution
 
  • #3
275
95
Why not use the law of cosines? Find the angle between the short sides.

## 38 = 3^2 + 4^2 - 2(3)(4)cos(θ) ##

Now solve for θ.
 
  • #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666
Why not use the law of cosines? Find the angle between the short sides.

## 38 = 3^2 + 4^2 - 2(3)(4)cos(θ) ##

Now solve for θ.
There's a typo in the equation above. The 38 should also be squared.
 
  • #5
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,257
974
There's a typo in the equation above. The 38 should also be squared.
No. It's ##\ \sqrt{38}\ ## which is being squared.
 
  • #6
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666
No. It's ##\ \sqrt{38}\ ## which is being squared.
Missed the root in the OP.
 
  • #7
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,753
5,035
taking sine both side , sin2C = sin(A+B) = sin(C),
I guess you meant sin 2C > sin(A+B), but that does not follow. Once the angle exceeds 90 degrees the sine function is decreasing. Indeed, sin(2C) would be < sin(A+B) here.
cosc > (1/2) therefore angle C> 60°
That's backwards. If sin(2C) were > sin(A+B), it would follow that C is less than 60.

@mfig's method is fine, but you do not need to solve for theta. Just show that the longest side is too long for a 120 angle.
 

Related Threads on Question from trigonometry -- prove that the largest angle is greater than 120°

  • Last Post
Replies
6
Views
1K
Replies
6
Views
13K
Replies
2
Views
3K
Replies
2
Views
5K
  • Last Post
Replies
6
Views
24K
Replies
1
Views
4K
Replies
2
Views
2K
Replies
3
Views
4K
Replies
4
Views
15K
Top