Questions: Miguel needs to fix a window screen that is 23 feet above. The ladder he uses makes a 75° angle with the ground. What is the shortest possible length of the ladder if the top of it is 23 feet off the ground? Round to the nearest whole number. 6 ft 22 ft 24 ft 89 ft

Miguel needs to fix a window screen that is 23 feet above. The ladder he uses makes a 75° angle with the ground. What is the shortest possible length of the ladder if the top of it is 23 feet off the ground? Round to the nearest whole number.
6 ft
22 ft
24 ft
89 ft

Transcript text: Miguel needs to fix a window screen that is 23 feet above. The ladder he uses makes a $75^{\circ}$ angle with the ground. What is the shortest possible length of the ladder if the top of it is 23 feet off the ground? Round to the nearest whole number. 6 ft 22 ft 24 ft 89 ft

Solution

Solution Steps

Step 1: Identify the given information

The height of the window is 23 feet. This is the opposite side of the 75° angle. The ladder forms a 75° angle with the ground. We want to find the length of the ladder, which is the hypotenuse.

Step 2: Set up the trigonometric equation

We can use the sine function because we have the opposite side and we want to find the hypotenuse. sin(75°) = opposite/hypotenuse sin(75°) = 23/hypotenuse

Step 3: Solve for the hypotenuse

hypotenuse = 23 / sin(75°) hypotenuse ≈ 23 / 0.9659 hypotenuse ≈ 23.8