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 angle in radians.
Let the angles of the triangle be (a – d) °, a° and (a + d) °.
We know that the sum of the angles of a triangle is 180°.
⇒ a – d + a + a + d = 180°
⇒ 3a = 180°
∴ a = 60°
Given
⇒ 120 – 2d = 1
⇒ 2d = 119
∴ d = 59.5
Hence, angles are:
⇒ (a – d) ° = 60° – 59.5° = 0.5°
⇒ a° = 60°
⇒ (a + d) ° = 60° + 59.5° = 119.5°
∴ Angles of triangle in radians: