Final answer:
Using the cosine of the given angle (80°) and the distance from the base of the ladder to the wall (4 feet), the length of the ladder is calculated to be approximately 23.03 feet.
Step-by-step explanation:
To find the length of the ladder, we can use trigonometry since we have an angle and one side of a right triangle. Using the angle and the side adjacent to it, we can apply the trigonometric function cosine. The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse, which in this case is the length of the ladder.
The formula to find the length of the ladder (hypotenuse) is as follows:
cos(θ) = (Adjacent Side) / (Hypotenuse)
Here, θ is 80°, and the Adjacent Side is 4 feet. Rearranging the formula to solve for the Hypotenuse gives us:
Hypotenuse = (Adjacent Side) / cos(θ)
Substitute the values into the formula to get:
Hypotenuse = 4 / cos(80°)
Calculating this with a calculator set to degree mode, we find the length of the ladder:
Hypotenuse = 4 / 0.173648
Hypotenuse ≈ 23.03 feet
Therefore, the length of the ladder is approximately 23.03 feet.