An electrician leans an extension ladder against the outside wall of a house so that it reach electric box 20 feet up. The ladder makes an angle of \( 77^{\circ} \) with the ground. Find the length ladder. Round your answer to the nearest hundredth of a foot if necessary.

To find the length of the ladder, we can use the sine function from trigonometry. The sine of the angle is equal to the opposite side (the height the ladder reaches) over the hypotenuse (the length of the ladder). Using the formula: \[ \sin(77^\circ) = \frac{\text{height}}{\text{length of ladder}} \] We can rearrange the formula to find the length of the ladder: \[ \text{length of ladder} = \frac{\text{height}}{\sin(77^\circ)} \] Plugging in the values: \[ \text{length of ladder} = \frac{20}{\sin(77^\circ)} \] Calculating \( \sin(77^\circ) \) gives approximately \( 0.9744 \). Thus, \[ \text{length of ladder} \approx \frac{20}{0.9744} \approx 20.53 \] The length of the ladder is approximately 20.53 feet. Now, let’s say you want to know a bit more! Ever wonder how long ladders have been around? Ladders date back to ancient Egypt, where they were depicted in wall paintings from around 5000 BC. They were initially made from simple materials like wood and rope. Fast forward a few millennia, and today we have all kinds of ladders from aluminum to fiberglass for safety around electricity! And when it comes to using ladders safely, always maintain three points of contact. This means you should have two hands and one foot or two feet and one hand in contact with the ladder at all times. It’s a lifesaver (literally)! And remember, don’t lean too far to one side, or you might be becoming a performer in the "ladder balancing act!"