IIT JEE , AIEEE Forum - Mathematics , Trignometry

bjsk20207

a²+ b²+ c²=8R^{2
What type of triangle it is?}

sreeee

right triangle

Mystic00

Right Angled triangle as the results implies sin²A + sin²B+ sin²c=2
which can be proved as a right angled triangle

venkat_tatolu

Given equn, becomes Sin²A+Sin²B+Sin²C=2 [by using sine rule]

2+2 CosA CosB CosC=2 [by transformations]

CosA CosB CosC=0

So either A or B or C = pi/2

Hence the triangle is right triangle.

krishna.gopal

Perfect answers.
For Right angle triangle a^2+b^2+c^2= 2c^2
And R=c/2
So 2c^2 = 8R^2