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

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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°

(180-60)=120 is also a solution, now you should think how to prove that particular solution

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.

SteamKing
Staff Emeritus
Homework Helper
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.

SammyS
Staff Emeritus
Homework Helper
Gold Member
There's a typo in the equation above. The 38 should also be squared.
No. It's ##\ \sqrt{38}\ ## which is being squared.

SteamKing
Staff Emeritus
Homework Helper
No. It's ##\ \sqrt{38}\ ## which is being squared.
Missed the root in the OP.

haruspex
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