Question An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of \( 66^{\circ} \) with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

To find the length of the ladder, we can use the sine function from trigonometry. The sine of an angle in a right triangle is the ratio of the opposite side (the height the ladder reaches) to the hypotenuse (the length of the ladder). We can set up the equation: \[ \sin(66^{\circ}) = \frac{22 \text{ feet}}{L} \] Where \( L \) is the length of the ladder. Rearranging this gives: \[ L = \frac{22}{\sin(66^{\circ})} \] Calculating this, \[ L \approx \frac{22}{0.9135} \approx 24.1 \text{ feet} \] So, the length of the ladder is approximately 24.1 feet. Now, for some extra insights: Imagine the moments when ladders were a vital invention! Dating back to ancient civilization, ladders helped builders reach new heights—think Egyptian pyramids and Roman aqueducts! They weren’t just tools; they represented the desire to rise above the ordinary, both literally and metaphorically. And who knew that those rickety wooden ladders narrated tales of ambition and innovation? When using a ladder, safety is paramount! Always ensure it's positioned on stable ground, and don't forget to maintain a three-point contact (two hands and one foot, or two feet and one hand) while climbing. A common mistake is leaning too far while reaching, which can lead to falls. Also, check the angle—55-75 degrees is generally safe to maintain stability while you work your magic, whether fixing a light or cleaning gutters!