Question

The measures of the angles of a triangle are in A.P. and the greatest is 5 times the smallest (least). Find the angles in degrees and radian.

Answer 1

Let the angles of the triangle be a – d, a, a + d in degrees.

Since sum of the angles of the triangle is 180°,

∴ a – d + a + a + d = 180° 

∴ 3a = 180°

∴ a = 60°

Also, a + d = 5 (a – d), where a = 60°

∴ 60° + d = 5(60° – d)

∴ 60° + d = 300° – 5d

∴ 6d = 240°

∴ d = 40°

∴ the angles of the triangle are

a – d = 60° − 40° = 20°,  a = 60°

and a + d = 60° + 40° = 100°

Now, θ° = ${\displaystyle {(\theta \times \frac{\pi }{180})}^{\text{c}}}$

20° = ${\displaystyle {(20\times \frac{\pi }{180})}^{\text{c}}={\left(\frac{\pi }{9}\right)}^{\text{c}}}$

60° = ${\displaystyle {(60\times \frac{\pi }{180})}^{\text{c}}={\left(\frac{\pi }{3}\right)}^{\text{c}}}$

100° = ${\displaystyle {(100\times \frac{\pi }{180})}^{\text{c}}={\left(\frac{5\pi }{9}\right)}^{\text{c}}}$