Question

convert the following angle to decimal degrees.
α = 72° 40 4
α ≈ □°
(round to 3 decimal places as needed.)

Explanation:

Step1: Convert minutes to degrees

We know that \(1^\circ = 60'\), so to convert \(40'\) to degrees, we divide by 60. So \(40'=\frac{40}{60}^\circ=\frac{2}{3}^\circ\approx0.6667^\circ\)

Step2: Convert seconds to degrees

We know that \(1^\circ = 3600''\), so to convert \(4''\) to degrees, we divide by 3600. So \(4''=\frac{4}{3600}^\circ=\frac{1}{900}^\circ\approx0.0011^\circ\)

Step3: Add all the degree parts together

The original angle has \(72^\circ\), plus the degrees from minutes and seconds. So \(\alpha = 72^\circ+\frac{40}{60}^\circ+\frac{4}{3600}^\circ\)
\[

$$\begin{align*} \alpha&=72 + \frac{40}{60}+\frac{4}{3600}\\ &=72+0.6667 + 0.0011\\ &=72.6678\\ &\approx72.668 \end{align*}$$

\]

Answer:

\(72.668\)