Chapter 1.2, Problem 1PSA

a.

To determine

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

Answer to Problem 1PSA

  $\theta =61°40^{\prime }$

Explanation of Solution

Given:

  $\theta =\left(61\frac{2}{3}\right)°$

Concept Used:

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

Calculation:

As per the given problem

  $\begin{array}{l}\theta =\left(61\frac{2}{3}\right)°\\ =61°+\left(\frac{2}{3}\right)°\\ =61°+{\left(\frac{2}{3}\times 60\right)}^{\prime }\\ =61°+40^{\prime }\\ =61°40^{\prime }\\ \Rightarrow \theta =61°40^{\prime }\end{array}$

Conclusion:

  $\theta =61°40^{\prime }$

b.

To determine

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

Answer to Problem 1PSA

  $\theta =71°{42}^{\prime }$

Explanation of Solution

Given:

  $\theta =\left(71.7\right)°$

Concept Used:

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

Calculation:

As per the given problem

  $\begin{array}{l}\theta =\left(71.7\right)°\\ =\left(71+\frac{7}{10}\right)°\\ =71°+\left(\frac{7}{10}\right)°\\ =71°+\frac{7}{10}\times 60^{\prime }\\ =71°+{\left(42\right)}^{\prime }\\ =71°{42}^{\prime }\\ \Rightarrow \theta =71°{42}^{\prime }\end{array}$

Conclusion:

  $\theta =71°{42}^{\prime }$