Apainter is using a ladder to reach the top of a house. if the house is 12 feet tall and the angle of the ladder needs to be at an angle of at least 60° and no greater than 75° to be safe, how far away should the painter place the ladder from the house? show your work

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°.

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step-by-step explanation: