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Chapter 2: Problem 28

Change each of the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a degree. $$ 21^{\circ} 15^{\prime} $$

Short Answer

Expert verified
The angle is 21.25掳 in decimal degrees.

Step by step solution

01

Understand the Components

The angle given, \(21^{\circ} 15^{\prime}\), consists of degrees and minutes. Here, \(21^{\circ}\) represents degrees, and \(15^{\prime}\) represents minutes. Our goal is to convert this notation into decimal degrees.
02

Convert Minutes to Decimal Degrees

Since 1 degree = 60 minutes, we can convert minutes to a decimal form of degrees using the formula: \( \text{Decimal Degrees} = \frac{\text{Minutes}}{60} \).So, for 15 minutes, the conversion is: \[ \text{Decimal Equivalent} = \frac{15}{60} = 0.25 \text{ degrees} \]
03

Combine Degrees and Decimal Conversion

Combine the whole degrees with the decimal equivalent of the minutes:\[ 21^{\circ} 15^{\prime} = 21 + 0.25 = 21.25^{\circ} \]
04

Round if Necessary

The answer is already rounded to the nearest hundredth, as 21.25 has two decimal places. No further rounding is necessary.

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Key Concepts

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

Degrees and Minutes
In the world of angles, degrees and minutes are used to specify precise measurements. Degrees BUSTRUCTION ERONSTRATIONgular algebra neednISTRACTON peers instantaneously.
Rounding
Rounding is an important skill to maintain precision and simplicity in numerical calculations. when angles are measured in decimal degrees, round the result to the desired level of precision.
Angle Conversion
Angle conversion, especially from degrees and minutes to decimal degrees, is a valuable skill in various fields.

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Most popular questions from this chapter

Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. The two equal sides of an isosceles triangle are each 42 centimeters. If the base measures 32 centimeters, find the height and the measure of the two equal angles.

Show that each of the following statements is true by transforming the left side of each one into the right side. $$ \sec \theta-\cos \theta=\frac{\sin ^{2} \theta}{\cos \theta} $$

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From here on, each Problem Set will end with a series of review problems. In mathematics, it is very important to review. The more you review, the better you will understand the topics we cover and the longer you will remember them. Also, there will be times when material that seemed confusing earlier will be less confusing the second time around. The problems that follow review material we covered in Section 1.2. Find the distance between the points \((3,-2)\) and \((-1,-4)\).

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