Chapter 1.2, Problem 2PSA

a.

To determine

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

Answer to Problem 2PSA

  $\theta =\left(132\frac{1}{2}\right)°$

Explanation of Solution

Given:

  $\theta =132°30^{\prime }$

Concept Used:

Calculation:

As per the given problem

  $\begin{array}{l}\theta =132°30^{\prime }\\ =132°+30^{\prime }\\ =132°+\left(\frac{1}{60}\times 30\right)°\\ =132°+\left(\frac{1}{2}\right)°\\ =\left(132\frac{1}{2}\right)°\\ \Rightarrow \theta =\left(132\frac{1}{2}\right)°\end{array}$

Conclusion:

  $\theta =\left(132\frac{1}{2}\right)°$

b.

To determine

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

Answer to Problem 2PSA

  $\theta =19.75°$

Explanation of Solution

Given:

  $\theta =19°45^{\prime }$

Concept Used:

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

Calculation:

As per the given problem

  $\begin{array}{l}\theta =19°45^{\prime }\\ =19°+45^{\prime }\\ =19°+\left(\frac{1}{60}\times 45\right)°\\ =19°+\left(\frac{3}{4}\right)°\\ =19°+\left(0.75\right)°\\ =\left(19.75\right)°\\ \Rightarrow \theta =19.75°\end{array}$

Conclusion:

  $\theta =19.75°$