# 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.

Basic Trigonometry

Trigonometry

Circular System

Relation between Sexagesimal and Circular

Conversion from Sexagesimal to Circular System

Conversion from Circular to Sexagesimal System