Answer:
More than 3.01 feet to 6 ft or less
Step-by-step explanation:
The expression for the angle we are using will be
60 ≤ Ф < 75 (it has to be at least 60, but less than 75)
The length of the ladder (12 ft) forms the hypotenuse of the triangle when leaned against the house. The distance from the ladder to the house is the side adjacent to the angle we are working with, so we can use the cosine function to solve.
Cos X = (adjacent side)/(hypotenuse)
Cos 60 = a/12
12 (Cos 60) = a
6 = a
6 feet is the furthest away he can place the ladder, any more and the angle will be less than 60°
Cos 75 = b/12
12(Cos 75) = b
3.01 = b
He must place the ladder more than 3.01 feet away or else the angle will be greater than 75°.
