An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. The ladder makes an angle of $71^{\circ}$ with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.
Answer
\(\boxed{\text{Final Answer: The length of the ladder is approximately 29.61 feet.}}\)
Step 1 ：Given: angle = $71^\circ$, height = 28 feet
Step 2 ：Convert angle to radians: angle_rad = $\frac{71 \times \pi}{180}$
Step 3 ：Calculate sine of the angle: sin(angle_rad) = $\sin(1.239183768915974)$
Step 4 ：Use sine function to find ladder length: ladder_length = $\frac{28}{\sin(1.239183768915974)}$
Step 5 ：Calculate ladder length: ladder_length = 29.61337907322678
Step 6 ：Round ladder length to the nearest hundredth: ladder_length_rounded = 29.61
Step 7 ：\(\boxed{\text{Final Answer: The length of the ladder is approximately 29.61 feet.}}\)
