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Question

The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.


Solution

Let A, B and C be the angles of triangle ABC.

We are given that A, B and C are in A.P.

Let A = a - d, B = a and C = a + d

According to the question,

A + B + C = 180

                 [By angle sum property]

a - d + a + a + d = 180

   3a=180 a=60 . . . (i)

Again,

least anglemean angle=1120

   ada=1120      119a=120d

   d=119 a120

   d=119120×60

=(1192)

=1192×π180=119 π360 radians

Now,

1=π180    radians

    B=a=60=π3   radians

A=ad=π3119 π360=π360 radians

C=a+d=π3+119π360=239π360   radians


Mathematics
RD Sharma
Standard XI

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