Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

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 solution is $40.18°$

Step1. Given information

$40°10\text{'}25\text{'}\text{'}$

Step2. Formula used

$1\text{'}=\left(\frac{1}{60}\right)° and 1\text{'}\text{'}=\left(\frac{1}{3600}\right)°$

Step3. Calculation

We have

$$\begin{gathered} 40°10\text{'}25\text{'}\text{'} \\ =40°+10.\left(\frac{1}{60}\right)°+25.\left(\frac{1}{3600}\right)° \\ =40°+\left(\frac{1}{6}\right)°+\left(\frac{1}{144}\right)° \\ =40°+.17°+.0069 \\ =40.1769° \\ =40.18° \end{gathered}$$