Chapter 1, Problem 4RP

a.

To determine

Convert given angle in degrees to degrees, minutes and seconds

Answer to Problem 4RP

The given angle will be $46°52^{\prime }30^{″}$

Explanation of Solution

Given information:

Change $46\frac{7}{8}°$ into degrees, minutes and seconds

Formula Used: $1°=60^{\prime }$ and $1^{\prime }=60^{″}$

Calculation:

Write $46\frac{7}{8}°$ as:

  $\begin{array}{l}\text{46}\frac{7}{8}°\\ \text{=46}\text{.875}°\\ =46°+0.875°\end{array}$

We have to remove decimal part, stepwise.

Convert $0.875°$ in minutes

Since, $1°=60^{\prime }$ , then

  $\begin{array}{l}46°+{\left(0.875\times 60\right)}^{\prime }\\ =46°+52.5^{\prime }\\ =46°+52^{\prime }+0.5^{\prime }\end{array}$

Now convert $0.5^{\prime }$ in seconds

Since, $1^{\prime }=60^{″}$ , then

  $\begin{array}{l}=46°+52^{\prime }+{\left(0.5\times 60\right)}^{\prime \text{}\prime }\\ =46°+52^{\prime }+30^{″}\end{array}$

Hence,

  $46\frac{7}{8}°=46°52^{\prime }30^{″}$

b.

To determine

Convert given angle in degrees and minutes to degrees

Answer to Problem 4RP

The given angle will be $132.10°$

Explanation of Solution

Given information:

Change $132°6^{\prime }$ to degrees

  $132°6^{\prime }$ can be written as:

  $\begin{array}{l}\text{132}°6^{\prime }\\ \text{=132}°\text{ + <msup><mo>6</mo><mo>′</mo></msup>}\end{array}$

Now, convert $6^{\prime }$ into degrees,

  $\begin{array}{l}\text{132}°\text{+}\left(\frac{6}{60}\right)°\left[\because 1^{\prime }=\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$60$}\right.\right)°\right]\\ =132°+0.10°\\ =132.10°\end{array}$