Question -
Answer -
Let the angles of the triangle be (a – d) o, ao and(a + d) o.
We know that, thesum of angles of triangle is 180°.
a – d + a + a + d =180°
3a = 180°
a = 180°/3
= 60o
Given:
Greatest angle = 5 ×least angle
Uponcross-multiplication,
Greatest angle /least angle = 5
(a+d)/(a-d) = 5
(60+d)/(60-d) = 5
By cross-multiplyingwe get,
60 + d = 300 – 5d
6d = 240
d = 240/6
= 40
Hence, angles are:
(a – d) ° = 60° –40° = 20°
a° = 60°
(a + d) ° = 60° +40° = 100°
∴ Anglesof triangle in radians:
(20 × π/180) rad =π/9
(60 × π/180) rad = π/3
(100 × π/180) rad =5π/9