 Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angled triangle. The sexagesimal system is one of the systems of measuring trigonometrical angles. It includes degrees, minutes, and seconds. Check out the solved example questions and more useful details about the sexagesimal system in the following sections.

What is Sexagesimal System?

The sexagesimal system is one of the systems of measuring angles. In Sexagesimal System, an angle is measured in degrees, minutes and seconds. If a straight line stands on another line and if the two adjacent angles thus formed are equal to one another, then each angle is called a right angle. Other systems of measuring angles are the centesimal system and circular system.

In the sexagesimal system, the angle that rotating ray traces making one complete revolution is taken to be 360°. A complete rotation means 360°. In this system, a right angle is divided into 90 equal parts and each part is called a degree (1°). A degree is divided into 60 equal parts and each part is called a Sexagesimal minute (1′). A minute is further divided into 60 equal parts, each part is called a Sexagesimal second (1″). In clear,

• 1 right angle = 90 degrees (90°)
• 1 degree = 60 minutes (60′)
• 1 minute = 60 seconds (60″)

Also, Check

Steps to Represent in Degrees, Minutes & Seconds

The following are the simple steps to express an angle in degrees, minutes and seconds.

• At first, divide the angle by taking the decimal point out.
• As one degree is equal to 60 minutes, multiply the amount of degree left by 60 minutes.
• One minute is 60 seconds. So, multiply the remaining minutes by 60 to get in seconds.

Problems on Sexagesimal System

Problem 1:
Express 75.13° in degree, minute and second.

Solution:
75.13° = 75° + (0.13)°
= 75° + (0.13 x 60′)
= 75° + 7.8′
= 75° + 7′ + (0.8)’
= 75° + 7′ + (0.8 x 60)”
= 75° + 7′ + 48″
Therefore, 75.13° = 75°7’48”

Problem 2:
Express 45.68° in degree, minute and second.

Solution:
45.68° = 45° + (0.68)°
= 45° + (0.68 x 60′)
= 45° + 40.8′
= 45° + 40′ + (0.8)’
= 45°+ 40′ + (0.8 x 60)”
= 45° + 40′ + 48″
Therefore, 45.68° = 45°40’48”.

Problem 3:
Express 62° in minutes.

Solution:
62° = 62 x 60
= 3720
Therefore, 62° is 3270′.