Question

A ladder against a building forms an angle of 54° with the ground. The base of the ladder is 7 ft from the building. Use the cosine ratio to determine the length of the ladder.

Answer 1

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.