Final answer:
Using the cosine ratio, the length of the ladder which forms a 54° angle with the ground and has a base 7 ft from the building is found to be approximately 11.95 feet.
Step-by-step explanation:
To determine the length of the ladder using the cosine ratio, we apply the trigonometric formula derived from the Pythagorean theorem that relates the adjacent side of a right-angled triangle (the base of the ladder) to the hypotenuse (the ladder's length) through the cosine of the given angle. The angle formed with the ground is 54° and the distance from the base of the ladder to the building is 7 ft.
The length of the ladder (L) can be found using the equation:
L = adjacent / cos(θ)
Plugging in the values, we get:
L = 7 ft / cos(54°) ≈ 7 ft / 0.586 ≈ 11.945 ft
So, the length of the ladder is approximately 11.95 feet.