Chapter 1.2, Problem 23PSC

To determine

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

Answer to Problem 23PSC

  $\theta =\left(72\frac{3}{8}\right)°$

Explanation of Solution

Given:

  $\theta =72°22^{\prime }30^{″}$

Concept Used:

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

Calculation:

As per the given problem

  $\begin{array}{l}\theta =72°22^{\prime }30^{″}\\ =72°+22^{\prime }+30^{″}\\ =72°+22^{\prime }+{\left(\frac{1}{2}\right)}^{\prime }\\ =72°+{\left(\frac{45}{2}\right)}^{\prime }\\ =72°+\left(\frac{1}{60}\times \frac{45}{2}\right)°\left[\because 1°=60\text{'}\Rightarrow 1\text{'}=\left(\frac{1}{60}\right)°\right]\\ =72°+\left(\frac{3}{8}\right)°\\ =72°+\left(\frac{3}{8}\right)°\\ =72°+\left(\frac{3}{8}\right)°\\ =\left(72\frac{3}{8}\right)°\\ \Rightarrow \theta =\left(72\frac{3}{8}\right)°\end{array}$

Conclusion:

  $\theta =\left(75\frac{3}{4}\right)°$