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Chapter 2: Problem 19

$$ \text { Convert each of the following to degrees and minutes. } $$ $$ 92.55^{\circ} $$

Short Answer

Expert verified
92.55掳 = 92掳 33'.

Step by step solution

01

Separate Whole Degrees and Decimal

First, identify the whole number part and the decimal part of the given degree measure. For \( 92.55^{\circ} \), the whole number part is 92 degrees and the decimal part is 0.55 degrees.
02

Convert Decimal to Minutes

To convert the decimal part of the degree to minutes, multiply by 60 (since 1 degree equals 60 minutes). So, compute: \[ 0.55 \times 60 = 33 \text{ minutes} \]
03

Combine Degrees and Minutes

Combine the whole number of degrees from Step 1 with the minutes calculated in Step 2. Thus, \( 92.55^{\circ} = 92^{\circ} 33' \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal to Minutes Conversion
When converting degrees with decimal points to degrees and minutes, it's essential to understand that the decimal part of a degree can be further broken down into minutes.
This is because one degree is composed of 60 minutes, akin to how an hour comprises 60 minutes.

Let's walk through the process:
  • Identify the decimal portion of your degree value. For example, in 92.55掳, the decimal is 0.55.
  • Multiply this decimal by 60 because there are 60 minutes in a full degree. In the case of 0.55, the calculation is 0.55 脳 60 = 33.
  • The resulting product gives you the number of minutes.
Thus, the decimal from degrees is successfully converted into minutes, making our conversion process clear and simple.
Degree Measurement
Degrees are a measure for angles, just as meters measure length. In navigation, astronomy, and various fields of study, angles are often expressed in degrees (掳).
A complete circle is divided into 360 degrees.

Here's how it works:
  • Each degree can further be divided into 60 smaller parts, called minutes 鈥� not to be confused with time minutes.
  • This division allows for more precision when describing the size of an angle. For instance, an angle could be written as 92掳, or more precisely as 92掳 33', with the minutes lending more meticulous detail.
This method of measuring helps communicate angles accurately, which is particularly useful in fields like trigonometry and physics.
Trigonometry Basics
Trigonometry is the mathematical discipline that studies relationships involving lengths and angles of triangles. It is fundamental for many advanced fields, including physics, architecture, and engineering.

At its core, trigonometry involves the use of degree measurement to define the angles in triangles:
  • Relationships such as sine, cosine, and tangent functions are used to relate the angles to side lengths. These functions depend heavily on angle measurement, often in degrees.
  • Understanding how to precisely convert angles into degrees and minutes, as covered earlier, allows for accurate calculation and interpretation of these functions.
Mastery of these basics not only aids in solving complex problems but also builds the foundation for further exploration in calculus and beyond.

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Most popular questions from this chapter

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