Convert the angle 139.32 to degrees, minutes, and seconds notation.

Question:

Convert the angle {eq}\displaystyle 139.32 {/eq} to degrees, minutes, and seconds notation.

Converting Decimal Degree into Degree-Minute-Second

To convert an angle from decimal degree form into degree-minute-second form, follow these steps below.

[1] First, for the degrees, use the whole number part of the given angle.

[2] Then, for the minutes, multiply the decimal part of the given angle by 60. Use the whole number part of the answer as minutes.

[3] Lastly, for the seconds, multiply the decimal part of the resulting answer from the previous step by 60. Use the whole number part of the answer as seconds.

Be sure to follow the rule on rounding when calculating the seconds part of the answer

Answer and Explanation: 1

We're asked to convert {eq}139.32^\circ {/eq} into {eq}\text{degrees-minutes-seconds} {/eq}.

From this decimal degree form, we can identify the degree as {eq}D = 139^\circ {/eq} which is the whole number of the given angle.

Then, multiply the decimal part of the given angle by {eq}60 {/eq} to identify the minutes, {eq}M {/eq} which is the whole number part of the answer.

$$\begin{align} M &= 0.32 \times 60 \\[0.2cm] M &= 19.2 \\[0.2cm] M &\approx 19' \\[0.2cm] \end{align} \\ $$

Next, from the decimal part of the resulting answer from the previous step, we multiply it again by {eq}60 {/eq} to identify the seconds, {eq}S {/eq} which is the whole number part of the answer.

$$\begin{align} S &= 0.2 \times 60 \\[0.2cm] S &= 12' \\[0.2cm] \end{align} \\ $$

Therefore, the measure of the given angle in {eq}\text{degrees-minutes-seconds} {/eq} is {eq}\bf{139^\circ\ 19'\ 12''} {/eq}.


Learn more about this topic:

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Types of Angles: Lesson for Kids

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Chapter 2 / Lesson 2
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Learn about the different types of angles. Discover what angles are, the different parts of an angle, and the measurement of an angle, then explore the characteristics of acute, right, obtuse, and straight angles.


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