Question

The angles of a triangle are in A.P. and the ratio of the number of degrees in the least to the number of radians in the greatest is 60:π. Find the angles of the triangle in degrees and radians.

Answer 1

let the angles are a-d,a,a+d.
so a-d+a+a+d=180 degree
3a=180 degree
a=60 degree
given that a-d/a=1/120
(60-d)/60=1/120
120-2d=1
d=119/2
so angles in radians will bve
60-119/2=1/2 degree,60degree,60+119/2 =239/2 degree
in radians anlgles will be
pi/360,pi/3,239pi/360

Answer 2

Let the angles of the triangle are (a - d), a, (a + d)

Now, in a triangle, the sum of all angles equal to 180 degree

=> (a - d) + a + (a + d) = 180

=> a - d + a + a + d = 180

=> 3a = 180

=> a = 180/3

=> a = 60

Now, the angle are (60 - d), 60, (60 + d)

Now, 60 - d is the least and 60 + d is the greatest angle.

Now, (60 + d)° = {(60 + d) * (π/180)}c

Given that, number of radians in the greatest angle/number of degrees in the least one = π/60

=> {(60 + d) * (π/180)}c /(60 - d) = π/60

=> (60 - d)/{(60 + d) * (π/180)}c = 60/π

=> 180(60 - d)/{(60 + d) * π} = 60/π

=> 180(60 - d)/(60 + d) = 60

=> (60 - d)/(60 + d) = 60/180

=> (60 - d)/(60 + d) = 1/3

=> 3(60 - d) = (60 + d)

=> 180 - 3d = 60 + d

=> 180 - 60 = 3d + d

=> 4d = 120

=> d = 120/4

=> d = 30

Now, the angles are (60 - 30), 60, (60 + 30) = 30, 60, 90