Chapter 1.2, Problem 20PSC

To determine

To Evaluate: The value of given angle in terms of degrees, minutes and seconds.

Answer to Problem 20PSC

  $\theta =15°{13}^{\prime }{20}^{\prime \text{}\prime }$

Explanation of Solution

Given:

  $\theta =\left(15\frac{2}{9}\right)°$

Concept Used:

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

Calculation:

As per the given problem

  $\begin{array}{l}\theta =\left(15\frac{2}{9}\right)°\\ =15°+\left(\frac{2}{9}\right)°\\ =15°+{\left(\frac{2}{9}\times 60\right)}^{\prime }\left[\because 1°=60\text{'}\right]\\ =15°+{\left(\frac{40}{3}\right)}^{\prime }\\ =15°+{\left(13\frac{1}{3}\right)}^{\prime }\\ =15°+{13}^{\prime }+{\left(\frac{1}{3}\right)}^{\prime }\\ =15°+{13}^{\prime }+{\left(\frac{1}{3}\times 60\right)}^{\prime \text{}\prime }\left[\because 1^{\prime }=60^{\prime \text{}\prime }\right]\\ =15°+{13}^{\prime }+{20}^{\prime \text{}\prime }\\ \Rightarrow \theta =15°{13}^{\prime }{20}^{\prime \text{}\prime }\end{array}$

Conclusion:

  $\theta =15°{13}^{\prime }{20}^{\prime \text{}\prime }$