In the sides of a triangle are in the ra...

In the sides of a triangle are in the ratio `1:sqrt(3):2,` then the measure of its greatest angle is `pi/6` (b)`pi/3` (c) `pi/2` (d) `(2pi)/3`

`pi/6`

`pi/2`

`pi/3`

`(2pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:

Let `a=1x,b=sqrt(3)x,c=2x`
now,by cosine law,
`2cb cos A=c^2+b^2-a^2`
=`2xx(2x)xx(sqrt(3)x) cos A=(2x)^2+(sqrt(3)x)^2-(x)^2`
`=>cosA=(4+3-1)/(2xx2xxsqrt(3))`
`=>cos A=(sqrt(3))/2`
`=>A=30^@`

Solving for B
...

Topper's Solved these Questions

SETS
RD SHARMA|Exercise Solved Examples And Exercises|218 Videos
SOME SPECIAL SERIES
RD SHARMA|Exercise Solved Examples And Exercises|69 Videos

Similar Questions

Explore conceptually related problems

If the sides of a triangle are proportional to 2,sqrt(6) and sqrt(3)-1, find the measure of its greatest angle.

cot^(-1)(-sqrt3)= (a) -pi/6 (b) (5pi)/6 (c) pi/3 (d) (2pi)/3

The sides of a triangle A B C are x , y ,\ sqrt(x^2+y^2+x y) respectively. The size of the greatest angle in radians is : (2pi)/3 (b) pi/3 (c) pi/2 (d) none of these

If the angles of a triangle are in A.P.then the measures of one of the angles in radians is (pi)/(6) b.(pi)/(3) c.(pi)/(2) d.(2 pi)/(3)

IF the lengths of the side of triangle are 3,5A N D7, then the largest angle of the triangle is pi/2 (b) (5pi)/6 (c) (2pi)/3 (d) (3pi)/4

In a triangle ABC the angle B is greater than angle C. If the measure of angles B and C satisfy the equation 4sin^3x-3sinx+0.75=0 then the measure of angle A is (A) pi/2 (B) (2p)/3 (C) pi/6 (D) (5pi)/6

sin^(-1)((-1)/2) (a) pi/3 (b) -pi/3 (c) pi/6 (d) -pi/6

In a hat harr ABC, if (c+a+b)(a+b-c)=ab then the measure of angel C is (pi)/(3)(b)(pi)/(6)(c)(2 pi)/(3) (d) (pi)/(2)

The period of cos5 theta is (a) pi^(2) (b) 2 pi (c) 2 pi/5 (d) pi/3

If (1-tantheta)/(1+tantheta) = 1/sqrt3 , where theta in (0, pi/2) , then theta = (a) pi/6 (b) pi/4 (c) pi/12 (d) pi/3

RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises

In a triangle A B C , if acosA=bcosB , show that the triangle is eithe...
Text Solution
|
If in triangle the angles are in the ratio as 1:2:3 , prove that the ...
Text Solution
|
In the sides of a triangle are in the ratio 1:sqrt(3):2, then the meas...
Text Solution
|
In any triangle A B C , prove that: (a^2sin(B-C))/(sinB+ sin C)+(b^2...
Text Solution
|
The angles of a triangle A B C are in AdotPdot and it is being given t...
Text Solution
|
In A B C , prove that (a – b)^2 cos^2 C/2 + (a + b)^2 sin^2 C/2 =c^2d...
Text Solution
|
In a A B C , if a=3,b=5 and c=7,find cos A ,cos B and cos C
Text Solution
|
If the sides a ,b ,c of a triangleABC are in HP, prove that sin^2(A/2)...
Text Solution
|
A person observes the angle of elevation of the peak of a hill from a ...
Text Solution
|
If in a triangle A B C , (2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a)...
Text Solution
|
In a triangle A B C , if cos A=(sinB)/(2sinC) , show that the triangle...
Text Solution
|
In any Delta A B C , prove that: (cosA)/(bcosC+c cosB)+(cosB)/(c cos...
Text Solution
|
In any DeltaA B C ,suma(sinB-sin C)= a^2+b^2+c^2 (b) a^2 (c) b...
Text Solution
|
In a Delta A B C , ifsinAa n dsinB are the roots of the equation c^2...
Text Solution
|
In any A B C , prove that: Delta=(a^2-b^2)/2dot(sinAsinB)/(sin(A-B))
Text Solution
|
In any triangle A B C , prove that:Delta=(b^2+c^2-a^2)/(4cota) .
Text Solution
|
In a triangle A B C ,a=4,b=3,/A=60^@ then c is root of the equation c^...
Text Solution
|
In any DeltaA B C ,2(bc cosA+ ca cosB+ab cosC) =
Text Solution
|
In any Delta A B C , the value of 2a csin((A-B+C)/2) is (a)a^2+b^2-c^...
Text Solution
|
In a DeltaA B C , if (c+a+b)(a+b-c)=a b , then the measure of angel C...
Text Solution
|