Angles of triangle are in A.P. If the number of degrees in the smalles

1.	Angles of triangle are in A.P. If the number of degrees in the smallest to the number of radians in the largest is as 60:π, then the smallest angle is
Answer» $\huge{ \red{➩}}$ 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

Angles of triangle are in A.P. If the number of degrees in the smallest to the number of radians in the largest is as 60:π, then the smallest angle is

Answer»

$\huge{ \red{➩}}$

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

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