Chapter 1.3, Problem 8PSA

a.

To determine

To Calculate: The value of given angle in terms of degrees and minutes.

Answer to Problem 8PSA

  $\theta =124°{36}^{\prime }$

Explanation of Solution

Given:

  $\theta =\left(124\frac{3}{5}\right)°$

Concept Used:

  $\begin{array}{l}1°=60\text{'}\\ 1^{\prime }=60^{″}\end{array}$

Calculation:

As per the given problem

  $\begin{array}{l}\theta =\left(124\frac{3}{5}\right)°\\ =124°+\left(\frac{3}{5}\right)°\\ =124°+{\left(\frac{3}{5}\times 60\right)}^{\prime }\\ =124°+{\left(36\right)}^{\prime }\\ =124°{\left(36\right)}^{\prime }\\ \Rightarrow \theta =124°{36}^{\prime }\end{array}$

Conclusion:

  $\theta =124°{36}^{\prime }$

b.

To determine

To Calculate: The value of given angle in terms of degrees.

Answer to Problem 8PSA

  $\theta =\left(84\frac{5}{6}\right)°$

Explanation of Solution

Given:

  $\theta =84°50^{\prime }$

Concept Used:

  $\begin{array}{l}1°=60\text{'}\\ 1^{\prime }=60^{″}\end{array}$

Calculation:

As per the given problem

  $\begin{array}{l}\theta =84°50^{\prime }\\ =84°+50^{\prime }\\ =84°+\left(\frac{1}{60}\times 50\right)°\\ =84°+\left(\frac{5}{6}\right)°\\ =\left(84\frac{5}{6}\right)°\\ \Rightarrow \theta =\left(84\frac{5}{6}\right)°\end{array}$

Conclusion:

  $\theta =15°1^{\prime }{20}^{\prime \text{}\prime }$