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If the angle of triangles are in the ratio 2:3:7, then the sides are in ratio of?

If the angle of triangles are in the ratio 2:3:7, then the sides are in ratio of?


 

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5 Answers

vivek kumar
57 Points
10 years ago

2x+3x+7x=180

angles are 30,45,105.

by sine formula a/sina=b/sinb=c/sinc

putting the values of angles we can find the ratio of sides

Swapnil Saxena
102 Points
10 years ago

If the angles of the triangle are in ratio 2:3:7 then assume them to be x

then 2x+3x+7x=180(Angle sum prop. of triagle)

12x=180 , x=15

then the individual angles will be 30,45,105

Now using Sine rule (Valid for all triangles)

Sin A/a = Sin B/b =Sin C/c (where a, b, c are the respective sides of the triangle)

Sin 30/a = Sin 45/b =Sin 105/c

=2a = root(2)b = ((3)1/2+1)/2(2)1/2 c

if 2a= root(2)b ==> b= root(2)a

if 2a = ((3)1/2+1)/2(2)1/2 c ==> c= 4(2)1/2 a/((3)1/2+1)

then the ration of the sides 1: root(2) : 4(2)1/2 /((3)1/2+1)


Pavan
11 Points
4 years ago
If angles are in ratio 1:2:3 then angles are 30;60;90. Then ratio of their sides are sin30:sin60:sin90=1:√3:2
Sanjay kumar saini
11 Points
4 years ago
suppose that angle of triangle
x,2x,3x
then will be x+2x+3x=180 degree---------(by triangle low)
so            6x=180degree
              x=30degree
then will be angle of triangle
x=30degree,          2x=2X30degree=60degree      and 3X30degree=80degree
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

If the angles of the triangle are in ratio 2:3:7 then assume them to be x
then 2x+3x+7x=180(Angle sum prop. of triagle)
12x=180 , x=15
then the individual angles will be 30,45,105
Now using Sine rule (Valid for all triangles)
Sin A/a = Sin B/b =Sin C/c (where a, b, c are the respective sides of the triangle)
Sin 30/a = Sin 45/b =Sin 105/c
=2a = root(2)b = ((3)1/2+1)/2(2)1/2 c
if 2a= root(2)b ==> b= root(2)a
if 2a = ((3)1/2+1)/2(2)1/2 c ==> c= 4(2)1/2 a/((3)1/2+1)
then the ration of the sides 1: root(2) : 4(2)1/2 /((3)1/2+1)

Thanks and Regards

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