Question

Jim is going to paint the side of his house. The height of his home is 22 feet and he has a ladder that extends to 25 feet. At what angle does Jim need to place the ladder against the ground so that the ladder reaches the top of his house?

Answer 1

Jim needs to place the ladder at an angle of arctan(22/Distance from the house) to reach the top of his house.

Step-by-step explanation:

To determine the angle at which Jim needs to place the ladder against the ground, we can use trigonometry. The ladder, with a length of 25 feet, is the hypotenuse of a right triangle, with the height of the house as the opposite side and the distance from the ladder's base to the house as the adjacent side. Using the tangent function, we can calculate the angle:

Tan(angle) = Opposite/Adjacent = Height/Distance from the house

Tan(angle) = 22/Distance from the house

Let's solve for the angle:

Angle = arctan(Height/Distance from the house) = arctan(22/Distance from the house)

Therefore, Jim needs to place the ladder at an angle of arctan(22/Distance from the house) to reach the top of his house.

Answer 2

Jim might need to place the ladder at about a 77 degree angle to reach the top of his house.