Home
Class 12
MATHS
If in triangle the angles be to the one ...

If in triangle the angles be to the one another as `1:2:3` , prove that the corresponding sides are

A

`1:sqrt(3):2`

B

`2:sqrt(3):1`

C

`sqrt(3):2:1`

D

`3:2:1`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `(angleA)/(1)=(angleB)/(2)=(angleC)/(3)=(A+B+C)/(1+2+3)=(180^(@))/(6)=30^(@)`
`thereforeangleA=30^(@),angleB=60^(@),angleC=90^(@)`
By sine rule ,
`a:b:c=sinA:sinB:sinC`
`=sin30^(@):sin60^(@):sin90^(@)`
`=(1)/(2):(sqrt(3))/(2):1=1:sqrt(3):2`
Promotional Banner

Similar Questions

Explore conceptually related problems

If in triangle the angles are in the ratio as 1:2:3, prove that the corresponding sides are 1:sqrt(3):2

If the angles of a triangle are in the ratio 1:2:3 , find the ratio between corresponding sides :

If the angles of a triangle are in the ratio 1:2:3,the corresponding sides are in the ratio

If the angles of a triangle ABC are in the ratio 1:2:3. then the corresponding sides are in the ratio ?

Triangles having equal areas and having one side of one of the triangle; equal to one side of the other; have their corresponding sides equal.

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other.Prove that the triangles are congruent.

If A,B,C are the angles of a triangle and tan A=1,tan B=2, prove that tan C=3 If a,b,c are the corresponding sides,then prove that (a)/(sqrt(5))=(b)/(2sqrt(2))=(c)/(3)

If the ratio of the angle bisector segments of the two equiangular triangles are in the ratio of 3:2 then what is the ratio of the corresponding sides of the two triangles?

Theorem 6.3 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.