# Conversion from Circular to Sexagesimal System

Worked-out problems on the conversion from circular to sexagesimal system:

1. In a right-angled triangle the difference between two acute angles is 2π/5. Express these two angles in terms of radian and degree.

Solution:

Let the acute angles be xc and yc. (According to the condition of the problem:

x + y = π/2 and x - y = 2π/5

Solving these two equations we get;

x = 1/2 (π/2 + 2π/5)

x = 1/2 (5π + 4π/10)

x = 1/2 (9π/10)

x = 9π/20

and y = 1/2 (π/2 - 2π/5)

y = 1/2 (5π - 4π/10)

y = 1/2 (π/10)

y = π/20

Again, x = (9 × 180°)/20 = 81°

y = 180°/20 = 9°

2. The circular measure of an angle is π/8; find its value in sexagesimal systems.

Solution:

πc/8

We know, πc = 180°

πc/8 = 180°/8

πc/8 = 22.5° = 22° + 0.5°

[Now we will convert 0.5° to minute.

0.5° = (0.5 × 60)’ ; since 1° = 60’

= 30’]

πc/8 = 22° 30’

Therefore, the sexagesimal measures of the angle π/8 is 22° 30’

The above solved problems help us to learn in trigonometry, about the conversion from circular to sexagesimal system.