A surveyor measures an angle btw two lines and find it to be 43° 20' 05"
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To convert the angle $43^\circ 20' 05''$ to decimal degrees:
Step 1: Convert the minutes to degrees by dividing by $60$.
$$20' = \frac{20}{60}^\circ = 0.33333...^\circ$$
Step 2: Convert the seconds to degrees by dividing by $3600$.
$$05'' = \frac{5}{3600}^\circ = 0.001388...^\circ$$
Step 3: Add the degree, converted minutes, and converted seconds together.
$$43^\circ + 0.33333...^\circ + 0.001388...^\circ = 43.334722...^\circ$$
The angle in decimal degrees is:
$$\boxed{\text{43.334722... degrees}}$$
