Q. 23. - Precalculus Enhanced with Graphing Utilities

Question

In Problems 23–28, convert each angle to a decimal in degrees. Round your answer to two decimal places.

$40°10\text{'}25\text{'}\text{'}.$

Step-by-Step Solution

Answer

The decimal degrees of the given value is$40.17°$.

Step 1. Given Information.

The given value is

$40°10\text{'}25\text{'}\text{'}.$

Step 2. Calculation.

Because we know that

 $$\begin{gathered} 1\text{'}=\left(\frac{1}{60}\right)° \\ 1\text{'}\text{'}=\left(\frac{1}{60}\right)\text{'}=\left(\left(\frac{1}{60}\right)·\left(\frac{1}{60}\right)\right)°. \end{gathered}$$

Now, on converting the values we get,

$$\begin{gathered} 40°10\text{'}25\text{'}\text{'} \\ =40°+\left(\frac{10}{60}\right)°+\left(\frac{25}{3600}\right)°. \\ =40°+0.1667°+0.0069°. \\ =40.1763°. \\ =40.17° \end{gathered}$$

The angle is $40.17°$.