Question

23) An extension ladder forming a 60° angle with the ground is placed against

Answer 1

Answer: the length of the extended ladder is 8√3 feet or 13.9 feet

the distance between the wall and the bottom of the ladder is 4√3 feet or 6.9 feet

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the extended length of the ladder h, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 60 = 12/h

√3/2 = 12/h

h = 12 × 2/√3 = 24√3

h = 24√3 × √3/√3

h = 8√3

To determine the distance between the wall and the bottom of the ladder d, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse.

Therefore,

Cos 60 = d/8√3

0.5 = d/8√3

d = 0.5 × 8√3

d = 4√3