Trigonometry

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

karan parekh

14 Years agoGrade

5 Answers

vivek kumar

14 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

14 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

8 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

8 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

5 Years 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